1.
Physics
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Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
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Quantum mechanics
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Quantum mechanics, including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large scales, early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. In 1803, Thomas Young, an English polymath, performed the famous experiment that he later described in a paper titled On the nature of light. This experiment played a role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays, Plancks hypothesis that energy is radiated and absorbed in discrete quanta precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, ludwig Boltzmann independently arrived at this result by considerations of Maxwells equations. However, it was only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmanns statistical interpretation of thermodynamics and proposed what is now called Plancks law, following Max Plancks solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohrs theory of structure, introducing elliptical orbits. This phase is known as old quantum theory, according to Planck, each energy element is proportional to its frequency, E = h ν, where h is Plancks constant. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right rather than a sizable discovery. He won the 1921 Nobel Prize in Physics for this work, lower energy/frequency means increased time and vice versa, photons of differing frequencies all deliver the same amount of action, but do so in varying time intervals. High frequency waves are damaging to human tissue because they deliver their action packets concentrated in time, the Copenhagen interpretation of Niels Bohr became widely accepted. In the mid-1920s, developments in mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory, out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons
3.
Identical particles
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Identical particles, also called indistinguishable or indiscernible particles, are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to particles such as electrons, composite subatomic particles such as atomic nuclei, as well as atoms. Quasiparticles also behave in this way, although all known indistinguishable particles are tiny, there is no exhaustive list of all possible sorts of particles nor a clear-cut limit of applicability, as explored in quantum statistics. There are two categories of identical particles, bosons, which can share quantum states, and fermions. Examples of bosons are photons, gluons, phonons, helium-4 nuclei, examples of fermions are electrons, neutrinos, quarks, protons, neutrons, and helium-3 nuclei. The fact that particles can be identical has important consequences in statistical mechanics, calculations in statistical mechanics rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles, for example, the indistinguishability of particles has been proposed as a solution to Gibbs mixing paradox. There are two methods for distinguishing between particles, the first method relies on differences in the intrinsic physical properties of the particles, such as mass, electric charge, and spin. If differences exist, it is possible to distinguish between the particles by measuring the relevant properties, however, it is an empirical fact that microscopic particles of the same species have completely equivalent physical properties. For instance, every electron in the universe has exactly the electric charge. Even if the particles have equivalent physical properties, there remains a second method for distinguishing between particles, which is to track the trajectory of each particle. As long as the position of particle can be measured with infinite precision. The problem with the approach is that it contradicts the principles of quantum mechanics. According to quantum theory, the particles do not possess definite positions during the periods between measurements, instead, they are governed by wavefunctions that give the probability of finding a particle at each position. As time passes, the wavefunctions tend to spread out and overlap, once this happens, it becomes impossible to determine, in a subsequent measurement, which of the particle positions correspond to those measured earlier. The particles are said to be indistinguishable. What follows is an example to make the above discussion concrete, let n denote a complete set of quantum numbers for specifying single-particle states For simplicity, consider a system composed of two identical particles. Suppose that one particle is in the state n1, and another is in the state n2, however, this expression implies the ability to identify the particle with n1 as particle 1 and the particle with n2 as particle 2
4.
Force
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In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity, force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity and it is measured in the SI unit of newtons and represented by the symbol F. The original form of Newtons second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. In an extended body, each part usually applies forces on the adjacent parts, such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of materials, or flow in fluids. In part this was due to an understanding of the sometimes non-obvious force of friction. A fundamental error was the belief that a force is required to maintain motion, most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years, the Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known, in order of decreasing strength, they are, strong, electromagnetic, weak, high-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotles view, the sphere contained four elements that come to rest at different natural places therein. Aristotle believed that objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground. He distinguished between the tendency of objects to find their natural place, which led to natural motion, and unnatural or forced motion
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Force carrier
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In particle physics, force carriers or messenger particles or intermediate particles are particles that give rise to forces between other particles. These particles are bundles of energy of a kind of field. There is one kind of field for every type of elementary particle, for instance, there is an electron field whose quanta are electrons, and an electromagnetic field whose quanta are photons. The force carrier particles that mediate the electromagnetic, weak, in particle physics, quantum field theories such as the Standard Model describe nature in terms of fields. Each field has a description as the set of particles of a particular type. The energy of a wave in a field is quantized, the Standard Model contains the following particles, each of which is an excitation of a particular field, Gluons, excitations of the strong gauge field. Photons, W bosons, and Z bosons, excitations of the gauge fields. Higgs bosons, excitations of one component of the Higgs field, several types of fermions, described as excitations of fermionic fields. In addition, composite particles such as mesons can be described as excitations of an effective field, gravity is not a part of the Standard Model, but it is thought that there may be particles called gravitons which are the excitations of gravitational waves. The status of this particle is still tentative, because the theory is incomplete, when one particle scatters off another, altering its trajectory, there are two ways to think about the process. In the field picture, we imagine that the field generated by one caused a force on the other. Alternatively, we can imagine one particle emitting a virtual particle which is absorbed by the other, the virtual particle transfers momentum from one particle to the other. The description of forces in terms of particles is limited by the applicability of the perturbation theory from which it is derived. In certain situations, such as low-energy QCD and the description of bound states, the electromagnetic force can be described by the exchange of virtual photons. The nuclear force binding protons and neutrons can be described by a field of which mesons are the excitations. At sufficiently large energies, the interaction between quarks can be described by the exchange of virtual gluons. Beta decay is an example of a due to the exchange of a W boson. Gravitation may be due to the exchange of virtual gravitons, in time, this relationship became known as Coulombs law
6.
Wave function
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A wave function in quantum physics is a description of the quantum state of a system. The wave function is a probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a function are the Greek letters ψ or Ψ. The wave function is a function of the degrees of freedom corresponding to some set of commuting observables. Once such a representation is chosen, the function can be derived from the quantum state. For a given system, the choice of which commuting degrees of freedom to use is not unique, some particles, like electrons and photons, have nonzero spin, and the wave function for such particles includes spin as an intrinsic, discrete degree of freedom. Other discrete variables can also be included, such as isospin and these values are often displayed in a column matrix. According to the principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions. The Schrödinger equation determines how wave functions evolve over time, a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name wave function, and gives rise to wave–particle duality, however, the wave function in quantum mechanics describes a kind of physical phenomenon, still open to different interpretations, which fundamentally differs from that of classic mechanical waves. The integral of this quantity, over all the degrees of freedom. This general requirement a wave function must satisfy is called the normalization condition, since the wave function is complex valued, only its relative phase and relative magnitude can be measured. In 1905 Einstein postulated the proportionality between the frequency of a photon and its energy, E = hf, and in 1916 the corresponding relation between photon momentum and wavelength, λ = h/p, the equations represent wave–particle duality for both massless and massive particles. In the 1920s and 1930s, quantum mechanics was developed using calculus and those who used the techniques of calculus included Louis de Broglie, Erwin Schrödinger, and others, developing wave mechanics. Those who applied the methods of linear algebra included Werner Heisenberg, Max Born, Schrödinger subsequently showed that the two approaches were equivalent. However, no one was clear on how to interpret it, at first, Schrödinger and others thought that wave functions represent particles that are spread out with most of the particle being where the wave function is large. This was shown to be incompatible with the scattering of a wave packet representing a particle off a target. While a scattered particle may scatter in any direction, it not break up
7.
Boson
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In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions, an important characteristic of bosons is that their statistics do not restrict the number of them that occupy the same quantum state. This property is exemplified by helium-4 when it is cooled to become a superfluid, unlike bosons, two identical fermions cannot occupy the same quantum space. Whereas the elementary particles that make up matter are fermions, the elementary bosons are force carriers that function as the glue holding matter together and this property holds for all particles with integer spin as a consequence of the spin–statistics theorem. This state is called Bose-Einstein condensation and it is believed that this property is the explanation of superfluidity. Bosons may be elementary, like photons, or composite. If it exists, a graviton must be a boson, composite bosons are important in superfluidity and other applications of Bose–Einstein condensates. This phenomenon is known as Bose-Einstein condensation and it is believed that this phenomenon is the secret behind superfluidity of liquids, Bosons differ from fermions, which obey Fermi–Dirac statistics. Two or more identical fermions cannot occupy the same quantum state, since bosons with the same energy can occupy the same place in space, bosons are often force carrier particles. Fermions are usually associated with matter Bosons are particles which obey Bose–Einstein statistics, thus fermions are sometimes said to be the constituents of matter, while bosons are said to be the particles that transmit interactions, or the constituents of radiation. The quantum fields of bosons are bosonic fields, obeying canonical commutation relations, the properties of lasers and masers, superfluid helium-4 and Bose–Einstein condensates are all consequences of statistics of bosons. Interactions between elementary particles are called fundamental interactions, the fundamental interactions of virtual bosons with real particles result in all forces we know. All known elementary and composite particles are bosons or fermions, depending on their spin, particles with spin are fermions. In the framework of quantum mechanics, this is a purely empirical observation. However, in quantum field theory, the spin–statistics theorem shows that half-integer spin particles cannot be bosons. In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities—when their wave functions overlap, at low densities, both types of statistics are well approximated by Maxwell–Boltzmann statistics, which is described by classical mechanics. All observed elementary particles are fermions or bosons. The observed elementary bosons are all bosons, photons, W and Z bosons, gluons
8.
Fermion
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In particle physics, a fermion is any subatomic particle characterized by Fermi–Dirac statistics. These particles obey the Pauli exclusion principle, fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics, a fermion can be an elementary particle, such as the electron, or it can be a composite particle, such as the proton. According to the theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons. Besides this spin characteristic, fermions have another specific property, they possess conserved baryon or lepton quantum numbers, therefore, what is usually referred to as the spin statistics relation is in fact a spin statistics-quantum number relation. As a consequence of the Pauli exclusion principle, only one fermion can occupy a quantum state at any given time. If multiple fermions have the same probability distribution, then at least one property of each fermion, such as its spin. Weakly interacting fermions can also display bosonic behavior under extreme conditions, at low temperature fermions show superfluidity for uncharged particles and superconductivity for charged particles. Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter, the Standard Model recognizes two types of elementary fermions, quarks and leptons. In all, the model distinguishes 24 different fermions, there are six quarks, and six leptons, along with the corresponding antiparticle of each of these. Mathematically, fermions come in three types - Weyl fermions, Dirac fermions, and Majorana fermions, most Standard Model fermions are believed to be Dirac fermions, although it is unknown at this time whether the neutrinos are Dirac or Majorana fermions. Dirac fermions can be treated as a combination of two Weyl fermions, in July 2015, Weyl fermions have been experimentally realized in Weyl semimetals. Composite particles can be bosons or fermions depending on their constituents, more precisely, because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion. Examples include the following, A baryon, such as the proton or neutron, the nucleus of a carbon-13 atom contains six protons and seven neutrons and is therefore a fermion. The atom helium-3 is made of two protons, one neutron, and two electrons, and therefore it is a fermion. The number of bosons within a composite made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. Fermionic or bosonic behavior of a particle is only seen at large distances. At proximity, where spatial structure begins to be important, a composite particle behaves according to its constituent makeup, fermions can exhibit bosonic behavior when they become loosely bound in pairs
9.
Pauli exclusion principle
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The Pauli exclusion principle is the quantum mechanical principle that states that two or more identical fermions cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, a more rigorous statement is that the total wave function for two identical fermions is antisymmetric with respect to exchange of the particles. This means that the function changes its sign if the space. The Pauli exclusion principle describes the behavior of all fermions, while bosons are subject to other principles, fermions include elementary particles such as quarks, electrons and neutrinos. Additionally, baryons such as protons and neutrons and some atoms are fermions, as such, the Pauli exclusion principle underpins many properties of everyday matter, from its large-scale stability, to the chemical behavior of atoms. Half-integer spin means that the angular momentum value of fermions is ℏ = h /2 π times a half-integer. In the theory of quantum mechanics fermions are described by antisymmetric states, in contrast, particles with integer spin have symmetric wave functions, unlike fermions they may share the same quantum states. Bosons include the photon, the Cooper pairs which are responsible for superconductivity, in the early 20th century it became evident that atoms and molecules with even numbers of electrons are more chemically stable than those with odd numbers of electrons. In the 1916 article The Atom and the Molecule by Gilbert N, in 1919 chemist Irving Langmuir suggested that the periodic table could be explained if the electrons in an atom were connected or clustered in some manner. Groups of electrons were thought to occupy a set of shells around the nucleus. In 1922, Niels Bohr updated his model of the atom by assuming that certain numbers of electrons corresponded to stable closed shells, Pauli looked for an explanation for these numbers, which were at first only empirical. At the same time he was trying to explain experimental results of the Zeeman effect in atomic spectroscopy and he found an essential clue in a 1924 paper by Edmund C. For this purpose he introduced a new two-valued quantum number, identified by Samuel Goudsmit, the Pauli exclusion principle with a single-valued many-particle wavefunction is equivalent to requiring the wavefunction to be antisymmetric. This implies A =0 when x = y, which is Pauli exclusion and it is true in any basis, since unitary changes of basis keep antisymmetric matrices antisymmetric, although strictly speaking, the quantity A is not a matrix but an antisymmetric second-order tensor. Conversely, if the diagonal quantities A are zero in every basis, to prove it, consider the matrix element ⟨ ψ |. This is zero, because the two particles have zero probability to both be in the superposition state | x ⟩ + | y ⟩. But this is equal to ⟨ ψ | x, x ⟩ + ⟨ ψ | x, y ⟩ + ⟨ ψ | y, x ⟩ + ⟨ ψ | y, y ⟩. The first and last terms on the side are diagonal elements and are zero
10.
Ferromagnetism
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Not to be confused with Ferrimagnetism, for an overview see Magnetism. Ferromagnetism is the mechanism by which certain materials form permanent magnets. In physics, several different types of magnetism are distinguished, an everyday example of ferromagnetism is a refrigerator magnet used to hold notes on a refrigerator door. The attraction between a magnet and ferromagnetic material is the quality of magnetism first apparent to the ancient world, permanent magnets are either ferromagnetic or ferrimagnetic, as are the materials that are noticeably attracted to them. Only a few substances are ferromagnetic, the common ones are iron, nickel, cobalt and most of their alloys, some compounds of rare earth metals, and a few naturally occurring minerals, including some varieties of lodestone. Historically, the term ferromagnetism was used for any material that could exhibit spontaneous magnetization and this general definition is still in common use. In particular, a material is ferromagnetic in this sense only if all of its magnetic ions add a positive contribution to the net magnetization. If some of the magnetic ions subtract from the net magnetization, if the moments of the aligned and anti-aligned ions balance completely so as to have zero net magnetization, despite the magnetic ordering, then it is an antiferromagnet. These alignment effects only occur at temperatures below a critical temperature. Among the first investigations of ferromagnetism are the works of Aleksandr Stoletov on measurement of the magnetic permeability of ferromagnetics. The table on the right lists a selection of ferromagnetic and ferrimagnetic compounds, ferromagnetism is a property not just of the chemical make-up of a material, but of its crystalline structure and microstructure. There are ferromagnetic metal alloys whose constituents are not themselves ferromagnetic, called Heusler alloys, conversely there are non-magnetic alloys, such as types of stainless steel, composed almost exclusively of ferromagnetic metals. Amorphous ferromagnetic metallic alloys can be made by rapid quenching of a liquid alloy. These have the advantage that their properties are isotropic, this results in low coercivity, low hysteresis loss, high permeability. One such typical material is a transition metal-metalloid alloy, made from about 80% transition metal, a relatively new class of exceptionally strong ferromagnetic materials are the rare-earth magnets. They contain lanthanide elements that are known for their ability to carry large magnetic moments in well-localized f-orbitals, a number of actinide compounds are ferromagnets at room temperature or exhibit ferromagnetism upon cooling. PuP is a paramagnet with cubic symmetry at room temperature, in its ferromagnetic state, PuPs easy axis is in the <100> direction. In NpFe2 the easy axis is <111>, above TC ≈500 K NpFe2 is also paramagnetic and cubic
11.
Classical mechanics
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In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology. Classical mechanics describes the motion of objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars. Within classical mechanics are fields of study that describe the behavior of solids, liquids and gases, Classical mechanics also provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When both quantum and classical mechanics cannot apply, such as at the level with high speeds. Since these aspects of physics were developed long before the emergence of quantum physics and relativity, however, a number of modern sources do include relativistic mechanics, which in their view represents classical mechanics in its most developed and accurate form. Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and these advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newtons work, particularly through their use of analytical mechanics. The following introduces the concepts of classical mechanics. For simplicity, it often models real-world objects as point particles, the motion of a point particle is characterized by a small number of parameters, its position, mass, and the forces applied to it. Each of these parameters is discussed in turn, in reality, the kind of objects that classical mechanics can describe always have a non-zero size. Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the degrees of freedom. However, the results for point particles can be used to such objects by treating them as composite objects. The center of mass of a composite object behaves like a point particle, Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space, non-relativistic mechanics also assumes that forces act instantaneously. The position of a point particle is defined with respect to a fixed reference point in space called the origin O, in space. A simple coordinate system might describe the position of a point P by means of a designated as r. In general, the point particle need not be stationary relative to O, such that r is a function of t, the time
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Werner Heisenberg
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Werner Karl Heisenberg was a German theoretical physicist and one of the key pioneers of quantum mechanics. He published his work in 1925 in a breakthrough paper, in the subsequent series of papers with Max Born and Pascual Jordan, during the same year, this matrix formulation of quantum mechanics was substantially elaborated. In 1927 he published his uncertainty principle, upon which he built his philosophy, Heisenberg was awarded the Nobel Prize in Physics for 1932 for the creation of quantum mechanics. He was a principal scientist in the Nazi German nuclear weapon project during World War II and he travelled to occupied Copenhagen where he met and discussed the German project with Niels Bohr. Following World War II, he was appointed director of the Kaiser Wilhelm Institute for Physics and he was director of the institute until it was moved to Munich in 1958, when it was expanded and renamed the Max Planck Institute for Physics and Astrophysics. He studied physics and mathematics from 1920 to 1923 at the Ludwig-Maximilians-Universität München, at Munich, he studied under Arnold Sommerfeld and Wilhelm Wien. At Göttingen, he studied physics with Max Born and James Franck and he received his doctorate in 1923, at Munich under Sommerfeld. He completed his Habilitation in 1924, at Göttingen under Born, at the event, Bohr was a guest lecturer and gave a series of comprehensive lectures on quantum atomic physics. There, Heisenberg met Bohr for the first time, and it had a significant, Heisenbergs doctoral thesis, the topic of which was suggested by Sommerfeld, was on turbulence, the thesis discussed both the stability of laminar flow and the nature of turbulent flow. The problem of stability was investigated by the use of the Orr–Sommerfeld equation and he briefly returned to this topic after World War II. Heisenbergs paper on the anomalous Zeeman effect was accepted as his Habilitationsschrift under Max Born at Göttingen, in his youth he was a member and Scoutleader of the Neupfadfinder, a German Scout association and part of the German Youth Movement. In August 1923 Robert Honsell and Heisenberg organized a trip to Finland with a Scout group of this association from Munich, Heisenberg arrived at Munich in 1919 as a member of Freikorps to fight the Bavarian Soviet Republic established a year earlier. Five decades later he recalled those days as youthful fun, like playing cops and robbers and so on, from 1924 to 1927, Heisenberg was a Privatdozent at Göttingen. His seminal paper, Über quantentheoretischer Umdeutung was published in September 1925 and he returned to Göttingen and with Max Born and Pascual Jordan, over a period of about six months, developed the matrix mechanics formulation of quantum mechanics. On 1 May 1926, Heisenberg began his appointment as a university lecturer and it was in Copenhagen, in 1927, that Heisenberg developed his uncertainty principle, while working on the mathematical foundations of quantum mechanics. On 23 February, Heisenberg wrote a letter to fellow physicist Wolfgang Pauli, in his paper on the uncertainty principle, Heisenberg used the word Ungenauigkeit. In 1927, Heisenberg was appointed ordentlicher Professor of theoretical physics and head of the department of physics at the Universität Leipzig, in his first paper published from Leipzig, Heisenberg used the Pauli exclusion principle to solve the mystery of ferromagnetism. Slater, Edward Teller, John Hasbrouck van Vleck, Victor Frederick Weisskopf, Carl Friedrich von Weizsäcker, Gregor Wentzel, in early 1929, Heisenberg and Pauli submitted the first of two papers laying the foundation for relativistic quantum field theory
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Paul Dirac
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Paul Adrien Maurice Dirac OM FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions, Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger for the discovery of new productive forms of atomic theory. He also made significant contributions to the reconciliation of general relativity with quantum mechanics and he was regarded by his friends and colleagues as unusual in character. Albert Einstein said of him This balancing on the path between genius and madness is awful. He is regarded as one of the most significant physicists of the 20th century, Paul Adrien Maurice Dirac was born at his parents home in Bristol, England, on 8 August 1902, and grew up in the Bishopston area of the city. His father, Charles Adrien Ladislas Dirac, was an immigrant from Saint-Maurice, Switzerland and his mother, Florence Hannah Dirac, née Holten, the daughter of a ships captain, was born in Cornwall, England, and worked as a librarian at the Bristol Central Library. Paul had a sister, Béatrice Isabelle Marguerite, known as Betty, and an older brother, Reginald Charles Félix, known as Felix. Dirac later recalled, My parents were terribly distressed, I didnt know they cared so much I never knew that parents were supposed to care for their children, but from then on I knew. Charles and the children were officially Swiss nationals until they became naturalised on 22 October 1919, Diracs father was strict and authoritarian, although he disapproved of corporal punishment. Dirac had a relationship with his father, so much so that after his fathers death, Dirac wrote, I feel much freer now. Charles forced his children to speak to him only in French, when Dirac found that he could not express what he wanted to say in French, he chose to remain silent. Dirac was educated first at Bishop Road Primary School and then at the all-boys Merchant Venturers Technical College, the school was an institution attached to the University of Bristol, which shared grounds and staff. It emphasised technical subjects like bricklaying, shoemaking and metal work and this was unusual at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express his gratitude. Dirac studied electrical engineering on a City of Bristol University Scholarship at the University of Bristols engineering faculty, shortly before he completed his degree in 1921, he sat the entrance examination for St Johns College, Cambridge. He passed, and was awarded a £70 scholarship, but this short of the amount of money required to live. Instead he took up an offer to study for a Bachelor of Arts degree in mathematics at the University of Bristol free of charge and he was permitted to skip the first year of the course owing to his engineering degree. In 1923, Dirac graduated, once again with first class honours, along with his £70 scholarship from St Johns College, this was enough to live at Cambridge. From 1925 to 1928 he held an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851 and he completed his PhD in June 1926 with the first thesis on quantum mechanics to be submitted anywhere
14.
Electromagnetic force
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Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as fields, magnetic fields. The other three fundamental interactions are the interaction, the weak interaction, and gravitation. The word electromagnetism is a form of two Greek terms, ἤλεκτρον, ēlektron, amber, and μαγνῆτις λίθος magnētis lithos, which means magnesian stone. The electromagnetic force plays a role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of forces between individual atoms and molecules in matter, and is a manifestation of the electromagnetic force. Electrons are bound by the force to atomic nuclei, and their orbital shapes. The electromagnetic force governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms, there are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential, although electromagnetism is considered one of the four fundamental forces, at high energy the weak force and electromagnetic force are unified as a single electroweak force. In the history of the universe, during the epoch the unified force broke into the two separate forces as the universe cooled. Originally, electricity and magnetism were considered to be two separate forces, Magnetic poles attract or repel one another in a manner similar to positive and negative charges and always exist as pairs, every north pole is yoked to a south pole. An electric current inside a wire creates a corresponding magnetic field outside the wire. Its direction depends on the direction of the current in the wire. A current is induced in a loop of wire when it is moved toward or away from a field, or a magnet is moved towards or away from it. While preparing for a lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. As he was setting up his materials, he noticed a compass needle deflected away from north when the electric current from the battery he was using was switched on. At the time of discovery, Ørsted did not suggest any explanation of the phenomenon. However, three later he began more intensive investigations
15.
Photon
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A photon is an elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force. The photon has zero rest mass and is moving at the speed of light. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a photon may be refracted by a lens and exhibit wave interference with itself. The quanta in a light wave cannot be spatially localized, some defined physical parameters of a photon are listed. The modern concept of the photon was developed gradually by Albert Einstein in the early 20th century to explain experimental observations that did not fit the classical model of light. The benefit of the model was that it accounted for the frequency dependence of lights energy. The photon model accounted for observations, including the properties of black-body radiation. In that model, light was described by Maxwells equations, in 1926 the optical physicist Frithiof Wolfers and the chemist Gilbert N. Lewis coined the name photon for these particles. After Arthur H. Compton won the Nobel Prize in 1927 for his studies, most scientists accepted that light quanta have an independent existence. In the Standard Model of particle physics, photons and other particles are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of particles, such as charge, mass and it has been applied to photochemistry, high-resolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers, in 1900, the German physicist Max Planck was studying black-body radiation and suggested that the energy carried by electromagnetic waves could only be released in packets of energy. In his 1901 article in Annalen der Physik he called these packets energy elements, the word quanta was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1905, Albert Einstein suggested that waves could only exist as discrete wave-packets. He called such a wave-packet the light quantum, the name photon derives from the Greek word for light, φῶς. Arthur Compton used photon in 1928, referring to Gilbert N. Lewis, the name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later in a physiological context. Although Wolferss and Lewiss theories were contradicted by many experiments and never accepted, in physics, a photon is usually denoted by the symbol γ
16.
Strong interaction
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At the range of 10−15 m, the strong force is approximately 137 times as strong as electromagnetism, a million times as strong as the weak interaction and 1038 times as strong as gravitation. The strong nuclear force holds most ordinary matter together because it confines quarks into hadron particles such as proton and neutron, in addition, the strong force binds neutrons and protons to create atomic nuclei. Most of the mass of a proton or neutron is the result of the strong force field energy. The strong interaction is observable at two ranges, on a scale, it is the force that binds protons and neutrons together to form the nucleus of an atom. On the smaller scale, it is the force that holds together to form protons, neutrons. In the latter context, it is known as the color force. The strong force inherently has such a strength that hadrons bound by the strong force can produce new massive particles. Thus, if hadrons are struck by particles, they give rise to new hadrons instead of emitting freely moving radiation. This property of the force is called color confinement, and it prevents the free emission of the strong force, instead, in practice. In the context of binding protons and neutrons together to form atomic nuclei, in this case, it is the residuum of the strong interaction between the quarks that make up the protons and neutrons. As such, the strong interaction obeys a quite different distance-dependent behavior between nucleons, from when it is acting to bind quarks within nucleons. The binding energy that is released on the breakup of a nucleus is related to the residual strong force and is harnessed as fission energy in nuclear power. The strong interaction is mediated by the exchange of particles called gluons that act between quarks, antiquarks, and other gluons. Gluons are thought to interact with quarks and other gluons by way of a type of charge called color charge. Color charge is analogous to electromagnetic charge, but it comes in three rather than one, which results in a different type of force, with different rules of behavior. These rules are detailed in the theory of quantum chromodynamics, which is the theory of quark-gluon interactions, after the Big Bang and during the electroweak epoch of the universe, the electroweak force separated from the strong force. A Grand Unified Theory is hypothesized to exist to describe this, but no theory has yet been successfully formulated. Before the 1970s, physicists were uncertain as to how the nucleus was bound together
17.
Quark
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A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation, they can be found only within hadrons, such as baryons and mesons. For this reason, much of what is known about quarks has been drawn from observations of the hadrons themselves, Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin. There are six types of quarks, known as flavors, up, down, strange, charm, top, up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay, the transformation from a higher mass state to a lower mass state. Because of this, up and down quarks are generally stable and the most common in the universe, whereas strange, charm, bottom, and top quarks can only be produced in high energy collisions. For every quark flavor there is a type of antiparticle, known as an antiquark. The quark model was proposed by physicists Murray Gell-Mann and George Zweig in 1964. Accelerator experiments have provided evidence for all six flavors, the top quark was the last to be discovered at Fermilab in 1995. The Standard Model is the theoretical framework describing all the known elementary particles. This model contains six flavors of quarks, named up, down, strange, charm, bottom, antiparticles of quarks are called antiquarks, and are denoted by a bar over the symbol for the corresponding quark, such as u for an up antiquark. As with antimatter in general, antiquarks have the mass, mean lifetime, and spin as their respective quarks. Quarks are spin- 1⁄2 particles, implying that they are fermions according to the spin-statistics theorem and they are subject to the Pauli exclusion principle, which states that no two identical fermions can simultaneously occupy the same quantum state. This is in contrast to bosons, any number of which can be in the same state, unlike leptons, quarks possess color charge, which causes them to engage in the strong interaction. The resulting attraction between different quarks causes the formation of composite particles known as hadrons, there are two families of hadrons, baryons, with three valence quarks, and mesons, with a valence quark and an antiquark. The most common baryons are the proton and the neutron, the blocks of the atomic nucleus. A great number of hadrons are known, most of them differentiated by their quark content, the existence of exotic hadrons with more valence quarks, such as tetraquarks and pentaquarks, has been conjectured but not proven. However, on 13 July 2015, the LHCb collaboration at CERN reported results consistent with pentaquark states, elementary fermions are grouped into three generations, each comprising two leptons and two quarks
18.
Gluon
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In lay terms, they glue quarks together, forming protons and neutrons. In technical terms, gluons are vector gauge bosons that mediate interactions of quarks in quantum chromodynamics. Gluons themselves carry the charge of the strong interaction. This is unlike the photon, which mediates the electromagnetic interaction, gluons therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than QED. The gluon is a boson, like the photon, it has a spin of 1. In quantum field theory, unbroken gauge invariance requires that gauge bosons have zero mass, the gluon has negative intrinsic parity. Unlike the single photon of QED or the three W and Z bosons of the interaction, there are eight independent types of gluon in QCD. This may be difficult to understand intuitively, quarks carry three types of color charge, antiquarks carry three types of anticolor. Gluons may be thought of as carrying both color and anticolor, but to understand how they are combined, it is necessary to consider the mathematics of color charge in more detail. A relevant illustration in the case at hand would be a gluon with a state described by. This is read as red–antiblue plus blue–antired, the color singlet state is, /3. In words, if one could measure the color of the state, there would be equal probabilities of it being red-antired, blue-antiblue, there are eight remaining independent color states, which correspond to the eight types or eight colors of gluons. Because states can be mixed together as discussed above, there are ways of presenting these states. One commonly used list is, These are equivalent to the Gell-Mann matrices, there are many other possible choices, but all are mathematically equivalent, at least equally complex, and give the same physical results. Technically, QCD is a theory with SU gauge symmetry. Quarks are introduced as spinors in Nf flavors, each in the representation of the color gauge group. The gluons are vectors in the adjoint representation of color SU, for a general gauge group, the number of force-carriers is always equal to the dimension of the adjoint representation. For the simple case of SU, the dimension of this representation is N2 −1, in terms of group theory, the assertion that there are no color singlet gluons is simply the statement that quantum chromodynamics has an SU rather than a U symmetry
19.
Quantum field theory
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QFT treats particles as excited states of the underlying physical field, so these are called field quanta. In quantum field theory, quantum mechanical interactions among particles are described by interaction terms among the corresponding underlying quantum fields and these interactions are conveniently visualized by Feynman diagrams, which are a formal tool of relativistically covariant perturbation theory, serving to evaluate particle processes. The first achievement of quantum theory, namely quantum electrodynamics, is still the paradigmatic example of a successful quantum field theory. Ordinarily, quantum mechanics cannot give an account of photons which constitute the prime case of relativistic particles, since photons have rest mass zero, and correspondingly travel in the vacuum at the speed c, a non-relativistic theory such as ordinary QM cannot give even an approximate description. Photons are implicit in the emission and absorption processes which have to be postulated, for instance, the formalism of QFT is needed for an explicit description of photons. In fact most topics in the development of quantum theory were related to the interaction of radiation and matter. However, quantum mechanics as formulated by Dirac, Heisenberg, and Schrödinger in 1926–27 started from atomic spectra, as soon as the conceptual framework of quantum mechanics was developed, a small group of theoreticians tried to extend quantum methods to electromagnetic fields. A good example is the paper by Born, Jordan & Heisenberg. The basic idea was that in QFT the electromagnetic field should be represented by matrices in the way that position. The ideas of QM were thus extended to systems having a number of degrees of freedom. The inception of QFT is usually considered to be Diracs famous 1927 paper on The quantum theory of the emission and absorption of radiation, here Dirac coined the name quantum electrodynamics for the part of QFT that was developed first. Employing the theory of the harmonic oscillator, Dirac gave a theoretical description of how photons appear in the quantization of the electromagnetic radiation field. Later, Diracs procedure became a model for the quantization of fields as well. These first approaches to QFT were further developed during the three years. P. Jordan introduced creation and annihilation operators for fields obeying Fermi–Dirac statistics and these differ from the corresponding operators for Bose–Einstein statistics in that the former satisfy anti-commutation relations while the latter satisfy commutation relations. The methods of QFT could be applied to derive equations resulting from the treatment of particles, e. g. the Dirac equation, the Klein–Gordon equation. Schweber points out that the idea and procedure of second quantization goes back to Jordan, in a number of papers from 1927, some difficult problems concerning commutation relations, statistics, and Lorentz invariance were eventually solved. The first comprehensive account of a theory of quantum fields, in particular
20.
Spin (physics)
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In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. Spin is one of two types of angular momentum in mechanics, the other being orbital angular momentum. In some ways, spin is like a vector quantity, it has a definite magnitude, all elementary particles of a given kind have the same magnitude of spin angular momentum, which is indicated by assigning the particle a spin quantum number. The SI unit of spin is the or, just as with classical angular momentum, very often, the spin quantum number is simply called spin leaving its meaning as the unitless spin quantum number to be inferred from context. When combined with the theorem, the spin of electrons results in the Pauli exclusion principle. Wolfgang Pauli was the first to propose the concept of spin, in 1925, Ralph Kronig, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested an physical interpretation of particles spinning around their own axis. The mathematical theory was worked out in depth by Pauli in 1927, when Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it. As the name suggests, spin was originally conceived as the rotation of a particle around some axis and this picture is correct so far as spin obeys the same mathematical laws as quantized angular momenta do. On the other hand, spin has some properties that distinguish it from orbital angular momenta. Although the direction of its spin can be changed, a particle cannot be made to spin faster or slower. The spin of a particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur if the internal charge of the particle were distributed differently from its mass. The conventional definition of the quantum number, s, is s = n/2. Hence the allowed values of s are 0, 1/2,1, 3/2,2, the value of s for an elementary particle depends only on the type of particle, and cannot be altered in any known way. The spin angular momentum, S, of any system is quantized. The allowed values of S are S = ℏ s = h 4 π n, in contrast, orbital angular momentum can only take on integer values of s, i. e. even-numbered values of n. Those particles with half-integer spins, such as 1/2, 3/2, 5/2, are known as fermions, while particles with integer spins. The two families of particles obey different rules and broadly have different roles in the world around us, a key distinction between the two families is that fermions obey the Pauli exclusion principle, that is, there cannot be two identical fermions simultaneously having the same quantum numbers
21.
Integer
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An integer is a number that can be written without a fractional component. For example,21,4,0, and −2048 are integers, while 9.75, 5 1⁄2, the set of integers consists of zero, the positive natural numbers, also called whole numbers or counting numbers, and their additive inverses. This is often denoted by a boldface Z or blackboard bold Z standing for the German word Zahlen, ℤ is a subset of the sets of rational and real numbers and, like the natural numbers, is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers, in algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In fact, the integers are the integers that are also rational numbers. Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, however, with the inclusion of the negative natural numbers, and, importantly,0, Z is also closed under subtraction. The integers form a ring which is the most basic one, in the following sense, for any unital ring. This universal property, namely to be an object in the category of rings. Z is not closed under division, since the quotient of two integers, need not be an integer, although the natural numbers are closed under exponentiation, the integers are not. The following lists some of the properties of addition and multiplication for any integers a, b and c. In the language of algebra, the first five properties listed above for addition say that Z under addition is an abelian group. As a group under addition, Z is a cyclic group, in fact, Z under addition is the only infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to Z. The first four properties listed above for multiplication say that Z under multiplication is a commutative monoid. However, not every integer has an inverse, e. g. there is no integer x such that 2x =1, because the left hand side is even. This means that Z under multiplication is not a group, all the rules from the above property table, except for the last, taken together say that Z together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of algebraic structure. Only those equalities of expressions are true in Z for all values of variables, note that certain non-zero integers map to zero in certain rings. The lack of zero-divisors in the means that the commutative ring Z is an integral domain
22.
Quantum state
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In quantum physics, quantum state refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, knowledge of the quantum state together with the rules for the systems evolution in time exhausts all that can be predicted about the systems behavior. A mixture of states is again a quantum state. Quantum states that cannot be written as a mixture of states are called pure quantum states. Mathematically, a quantum state can be represented by a ray in a Hilbert space over the complex numbers. The ray is a set of nonzero vectors differing by just a scalar factor, any of them can be chosen as a state vector to represent the ray. A unit vector is usually picked, but its phase factor can be chosen freely anyway, nevertheless, such factors are important when state vectors are added together to form a superposition. Hilbert space is a generalization of the ordinary Euclidean space and it all possible pure quantum states of the given system. If this Hilbert space, by choice of representation, is exhibited as a function space, a more complicated case is given by the spin part of a state vector | ψ ⟩ =12, which involves superposition of joint spin states for two particles with spin 1⁄2. A mixed quantum state corresponds to a mixture of pure states, however. Mixed states are described by so-called density matrices, a pure state can also be recast as a density matrix, in this way, pure states can be represented as a subset of the more general mixed states. For example, if the spin of an electron is measured in any direction, e. g. with a Stern–Gerlach experiment, the Hilbert space for the electrons spin is therefore two-dimensional. A mixed state, in case, is a 2 ×2 matrix that is Hermitian, positive-definite. These probability distributions arise for both mixed states and pure states, it is impossible in quantum mechanics to prepare a state in all properties of the system are fixed. This is exemplified by the uncertainty principle, and reflects a difference between classical and quantum physics. Even in quantum theory, however, for every observable there are states that have an exact. In the mathematical formulation of mechanics, pure quantum states correspond to vectors in a Hilbert space. The operator serves as a function which acts on the states of the system
23.
Electron
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The electron is a subatomic particle, symbol e− or β−, with a negative elementary electric charge. Electrons belong to the first generation of the lepton particle family, the electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the include a intrinsic angular momentum of a half-integer value, expressed in units of the reduced Planck constant. As it is a fermion, no two electrons can occupy the same state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of particles and waves, they can collide with other particles and can be diffracted like light. Since an electron has charge, it has an electric field. Electromagnetic fields produced from other sources will affect the motion of an electron according to the Lorentz force law, electrons radiate or absorb energy in the form of photons when they are accelerated. Laboratory instruments are capable of trapping individual electrons as well as electron plasma by the use of electromagnetic fields, special telescopes can detect electron plasma in outer space. Electrons are involved in applications such as electronics, welding, cathode ray tubes, electron microscopes, radiation therapy, lasers, gaseous ionization detectors. Interactions involving electrons with other particles are of interest in fields such as chemistry. The Coulomb force interaction between the positive protons within atomic nuclei and the negative electrons without, allows the composition of the two known as atoms, ionization or differences in the proportions of negative electrons versus positive nuclei changes the binding energy of an atomic system. The exchange or sharing of the electrons between two or more atoms is the cause of chemical bonding. In 1838, British natural philosopher Richard Laming first hypothesized the concept of a quantity of electric charge to explain the chemical properties of atoms. Irish physicist George Johnstone Stoney named this charge electron in 1891, electrons can also participate in nuclear reactions, such as nucleosynthesis in stars, where they are known as beta particles. Electrons can be created through beta decay of isotopes and in high-energy collisions. The antiparticle of the electron is called the positron, it is identical to the electron except that it carries electrical, when an electron collides with a positron, both particles can be totally annihilated, producing gamma ray photons. The ancient Greeks noticed that amber attracted small objects when rubbed with fur, along with lightning, this phenomenon is one of humanitys earliest recorded experiences with electricity. In his 1600 treatise De Magnete, the English scientist William Gilbert coined the New Latin term electricus, both electric and electricity are derived from the Latin ēlectrum, which came from the Greek word for amber, ἤλεκτρον
24.
Atomic orbital
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In quantum mechanics, an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atoms nucleus. The term, atomic orbital, may refer to the physical region or space where the electron can be calculated to be present. Each such orbital can be occupied by a maximum of two electrons, each with its own quantum number s. The simple names s orbital, p orbital, d orbital and these names, together with the value of n, are used to describe the electron configurations of atoms. They are derived from the description by early spectroscopists of certain series of alkali metal spectroscopic lines as sharp, principal, diffuse, Orbitals for ℓ >3 continue alphabetically, omitting j because some languages do not distinguish between the letters i and j. Atomic orbitals are the building blocks of the atomic orbital model. In this model the electron cloud of an atom may be seen as being built up in an electron configuration that is a product of simpler hydrogen-like atomic orbitals. The lowest possible energy an electron can take is therefore analogous to the frequency of a wave on a string. Higher energy states are similar to harmonics of the fundamental frequency. The electrons are never in a point location, although the probability of interacting with the electron at a single point can be found from the wave function of the electron. Particle-like properties, There is always a number of electrons orbiting the nucleus. Electrons jump between orbitals in a particle-like fashion, for example, if a single photon strikes the electrons, only a single electron changes states in response to the photon. The electrons retain particle-like properties such as, each state has the same electrical charge as the electron particle. Each wave state has a single discrete spin and this can depend upon its superposition. Thus, despite the popular analogy to planets revolving around the Sun, in addition, atomic orbitals do not closely resemble a planets elliptical path in ordinary atoms. A more accurate analogy might be that of a large and often oddly shaped atmosphere, atomic orbitals exactly describe the shape of this atmosphere only when a single electron is present in an atom. This is due to the uncertainty principle, atomic orbitals may be defined more precisely in formal quantum mechanical language
25.
John Hasbrouck Van Vleck
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Then he went to Harvard for graduate studies and earned a Ph. D degree in 1922. He joined the University of Minnesota as an assistant professor in 1923 and he also earned Honorary D. Sc. or D. Honoris Causa, degree from Wesleyan University in 1936. J. H. Van Vleck established the fundamentals of the mechanical theory of magnetism. He is regarded as the Father of Modern Magnetism, during World War II, J. H. Van Vleck worked on radar at the MIT Radiation Lab. He was half time at the Radiation Lab and half time on the staff at Harvard and this was to have important consequences not just for military radar systems but later for the new science of radioastronomy. J. H. Van Vleck participated in the Manhattan Project, in June 1942, J. Robert Oppenheimer held a summer study for confirming the concept and feasibility of nuclear weapon at the University of California, Berkeley. Eight theoretical scientists, including J. H. Van Vleck, from July to September, the theoretical study group examined and developed the principles of atomic bomb design. J. H. Van Vlecks theoretical work led to the establishment of the Los Alamos Nuclear Weapons Laboratory and he also served on the Los Alamos Review committee in 1943. The committee, established by General Leslie Groves, also consisted of W. K. Lewis of MIT, Chairman, E. L. Rose, of Jones & Lamson, E. B. Wilson of Harvard, and Richard C. However, it was not employed for the Fat Man bomb at Nagasaki, in 1961/62 he was George Eastman Visiting Professor at University of Oxford and Professorship of Balliol College. In 1950 he became member of the Royal Netherlands Academy of Arts. He was awarded the National Medal of Science in 1966 and the Lorentz Medal in 1974. For his contributions to the understanding of the behavior of electrons in solids, Van Vleck was awarded the Nobel Prize in Physics 1977, along with Philip W. Anderson. Van Vleck transformations and Van Vleck paramagnetism are also named after him, Van Vleck died in Cambridge, Massachusetts, aged 81. The Absorption of Radiation by Multiply Periodic Orbits, and its Relation to the Correspondence Principle, some Extensions of the Correspondence Principle, Physical Review, vol. 24, Issue 4, pp. 330–346 The Absorption of Radiation by Multiply Periodic Orbits, and its Relation to the Correspondence Principle, calculation of Absorption by Multiply Periodic Orbits, Physical Review, vol. 24, Issue 4, pp. 347–365 Quantum Principles and Line Spectra,14, pp. 178–188 He was awarded the Irving Langmuir Award in 1965, the National Medal of Science in 1966 and elected a Foreign Member of the Royal Society in 1967. He was awarded the Elliott Cresson Medal in 1971, the Lorentz Medal in 1974, J. H. Van Vleck and his wife Abigail were also important art collectors, particularly in the medium of Japanese woodblock prints, known as Van Vleck Collection
26.
Antiferromagnetism
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This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. Generally, antiferromagnetic order may exist at low temperatures, vanishing at and above a certain temperature. Above the Néel temperature, the material is typically paramagnetic, when no external field is applied, the antiferromagnetic structure corresponds to a vanishing total magnetization. Although the net magnetization should be zero at a temperature of absolute zero, the magnetic susceptibility of an antiferromagnetic material typically shows a maximum at the Néel temperature. In contrast, at the transition between the ferromagnetic to the paramagnetic phases the susceptibility will diverge, in the antiferromagnetic case, a divergence is observed in the staggered susceptibility. Various microscopic interactions between the magnetic moments or spins may lead to antiferromagnetic structures, in the simplest case, one may consider an Ising model on a bipartite lattice, e. g. the simple cubic lattice, with couplings between spins at nearest neighbor sites. Depending on the sign of that interaction, ferromagnetic or antiferromagnetic order will result, geometrical frustration or competing ferro- and antiferromagnetic interactions may lead to different and, perhaps, more complicated magnetic structures. Antiferromagnetic materials occur commonly among transition metal compounds, especially oxides, examples include hematite, metals such as chromium, alloys such as iron manganese, and oxides such as nickel oxide. There are also numerous examples among high nuclearity metal clusters, organic molecules can also exhibit antiferromagnetic coupling under rare circumstances, as seen in radicals such as 5-dehydro-m-xylylene. Unlike ferromagnetism, anti-ferromagnetic interactions can lead to multiple optimal states, in one dimension, the anti-ferromagnetic ground state is an alternating series of spins, up, down, up, down, etc. Yet in two dimensions, multiple ground states can occur, consider an equilateral triangle with three spins, one on each vertex. If each spin can take on two values, there are 23 =8 possible states of the system, six of which are ground states. The two situations which are not ground states are all three spins are up or are all down. In any of the six states, there will be two favorable interactions and one unfavorable one. This illustrates frustration, the inability of the system to find a ground state. This type of behavior has been found in minerals that have a crystal stacking structure such as a Kagome lattice or hexagonal lattice. Synthetic antiferromagnets are artificial antiferromagnets consisting of two or more thin ferromagnetic layers separated by a nonmagnetic layer, due to dipole coupling of the ferromagnetic layers results in antiparallel alignment of the magnetization of the ferromagnets. Antiferromagnetism plays a role in giant magnetoresistance, as had been discovered in 1988 by the Nobel prize winners Albert Fert
27.
Dihydrogen cation
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The hydrogen molecular ion, dihydrogen cation, or H+2, is the simplest molecular ion. It is composed of two positively charged protons and one negatively charged electron, and can be formed from ionization of a hydrogen molecule. The analytical solutions for the eigenvalues are a generalization of the Lambert W function. Thus, the case of clamped nuclei can be completely done analytically using a computer algebra system within an experimental mathematics approach, consequently, it is included as an example in most quantum chemistry textbooks. The first successful quantum mechanical treatment of H+2 was published by the Danish physicist Øyvind Burrau in 1927, earlier attempts using the old quantum theory had been published in 1922 by Karel Niessen and Wolfgang Pauli, and in 1925 by Harold Urey. In 1928, Linus Pauling published a review putting together the work of Burrau with the work of Walter Heitler, bonding in H+2 can be described as a covalent one-electron bond, which has a formal bond order of one half. The ion is formed in molecular clouds in space, and is important in the chemistry of the interstellar medium. The simplest electronic Schrödinger wave equation for the molecular ion H+2 is modeled with two fixed nuclear centers, labeled A and B, and one electron. An additive term 1/R, which is constant for fixed internuclear distance R, has been omitted from the potential V, the distances between the electron and the nuclei are denoted ra and rb. In atomic units the equation is ψ = E ψ with V = −1 r a −1 r b. We can choose the midpoint between the nuclei as the origin of coordinates and it follows from general symmetry principles that the wave functions can be characterized by their symmetry behavior with respect to space inversion. There are wave functions ψ+, which are symmetric with respect to inversion, and there are wave functions ψ−. The symmetry-adapted wave functions satisfy the same Schrödinger equation, the ground state of H+2 is denoted X2Σ+ g or 1sσg and it is symmetric. There is also the first excited state A2Σ+ u, which is antisymmetric, occurring here denote just the symmetry behavior under space inversion. Their use is standard practice for the designation of electronic states of molecules, whereas for atomic states the terms even. The lead term 4/eRe−R was first obtained by the Holstein–Herring method, similarly, asymptotic expansions in powers of 1/R have been obtained to high order by Cizek et al. for the lowest ten discrete states of the hydrogen molecular ion. These are of importance in stellar and atmospheric physics. The energies for the lowest discrete states are shown in the graph above, the red solid lines are 2Σ+ g states
28.
Ising model
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The Ising model, named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic spins that can be in one of two states, the spins are arranged in a graph, usually a lattice, allowing each spin to interact with its neighbors. The model allows the identification of phase transitions, as a model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition, the Ising model was invented by the physicist Wilhelm Lenz, who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model has no phase transition and was solved by Ising himself in his 1924 thesis, the two-dimensional square lattice Ising model is much harder, and was given an analytic description much later, by Lars Onsager. It is usually solved by a method, although there exist different approaches. In dimensions greater than four, the transition of the Ising model is described by mean field theory. Consider a set of lattice sites Λ, each with a set of adjacent sites forming a d-dimensional lattice, for each lattice site k ∈ Λ there is a discrete variable σk such that σk ∈, representing the sites spin. A spin configuration, σ = k ∈ Λ is an assignment of value to each lattice site. For any two adjacent sites i, j ∈ Λ one has an interaction Jij, also a site j ∈ Λ has an external magnetic field hj interacting with it. The notation <ij> indicates that sites i and j are nearest neighbors, the magnetic moment is given by µ. For a function f of the spins, one denotes by ⟨ f ⟩ β = ∑ σ f P β the expectation of f, the configuration probabilities Pβ represent the probability of being in a state with configuration σ in equilibrium. The minus sign on each term of the Hamiltonian function H is conventional, in a ferromagnetic Ising model, spins desire to be aligned, the configurations in which adjacent spins are of the same sign have higher probability. In an antiferromagnetic model, adjacent spins tend to have opposite signs, the sign convention of H also explains how a spin site j interacts with the external field. Namely, the spin site wants to line up with the external field, Ising models are often examined without an external field interacting with the lattice, that is, h =0 for all j in the lattice Λ. Using this simplification, our Hamiltonian becomes, H = − ∑ ⟨ i j ⟩ J i j σ i σ j. When the external field is zero, h =0, the Ising model is symmetric under switching the value of the spin in all the lattice sites. Another common simplification is to assume all of the nearest neighbors <ij> have the same interaction strength
29.
Valence bond theory
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In chemistry, valence bond theory is one of two basic theories, along with molecular orbital theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule, in 1916, G. N. Lewis proposed that a chemical bond forms by the interaction of two shared bonding electrons, with the representation of molecules as Lewis structures. In 1927 the Heitler–London theory was formulated which for the first time enabled the calculation of bonding properties of the hydrogen molecule H2 based on quantum mechanical considerations. Specifically, Walter Heitler determined how to use Schrödingers wave equation to show how two hydrogen atom wavefunctions join together, with plus, minus, and exchange terms, to form a covalent bond. He then called up his associate Fritz London and they worked out the details of the theory over the course of the night. Later, Linus Pauling used the pair bonding ideas of Lewis together with Heitler–London theory to two other key concepts in VB theory, resonance and orbital hybridization. Resonance theory was criticized as imperfect by Soviet chemists during the 1950s, according to this theory a covalent bond is formed between the two atoms by the overlap of half filled valence atomic orbitals of each atom containing one unpaired electron. A valence bond structure is similar to a Lewis structure, but where a single Lewis structure cannot be written, each of these VB structures represents a specific Lewis structure. This combination of valence bond structures is the point of resonance theory. Valence bond theory considers that the atomic orbitals of the participating atoms form a chemical bond. Because of the overlapping, it is most probable that electrons should be in the bond region, valence bond theory views bonds as weakly coupled orbitals. Valence bond theory is typically easier to employ in ground state molecules, the inner-shell orbitals and electrons remain essentially unchanged during the formation of bonds. The overlapping atomic orbitals can differ, the two types of overlapping orbitals are sigma and pi. Sigma bonds occur when the orbitals of two shared electrons overlap head-to-head, pi bonds occur when two orbitals overlap when they are parallel. For example, a bond between two electrons is a sigma bond, because two spheres are always coaxial. In terms of order, single bonds have one sigma bond, double bonds consist of one sigma bond and one pi bond. However, the orbitals for bonding may be hybrids
30.
Edmund Clifton Stoner
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Edmund Clifton Stoner FRS was a British theoretical physicist. He is principally known for his work on the origin and nature of itinerant ferromagnetism, including the electron theory of ferromagnetism. Stoner was born in Esher, Surrey, the son of cricketer Arthur Hallett Stoner and he won a scholarship to Bolton School and then attended University of Cambridge in 1918, graduating in 1921. After graduation, he worked at the Cavendish Laboratory on the absorption of X-rays by matter and electron energy levels, Stoner was appointed a Lecturer in the Department of Physics at the University of Leeds in 1932, becoming Professor of Theoretical Physics there in 1939. He did some work in astrophysics and computed a limit for the mass of white dwarf stars in 1930. Most of his research, however, was on magnetism, where, starting in 1938 and he is also known for his discovery of the Chandrasekhar limit before S. Chandrasekhar. The E C Stoner building at the University of Leeds is named after him and he was elected a Fellow of the Royal Society in May 1937. Stoner had been diagnosed with diabetes in 1919 and he controlled it with diet until 1927, when insulin treatment became available. Electron bands can spontaneously split into up and down spins and this happens if the relative gain in exchange interaction is larger than the loss in kinetic energy. The Stoner parameter which is a measure of the strength of the correlation is denoted I. Finally k is the wavenumber as the bands are in wavenumber-space. If more electrons favour one of the states this will create magnetism, the electrons obey Fermi–Dirac statistics so when the above formulas are summed over all k -space then the Stoner criterion for ferromagnetism can be established. The distribution of electrons among atomic levels, Philosophical Magazine 48, the limiting density of white dwarf stars, Philosophical Magazine 7, pp. 63–70. The equilibrium of dense stars, Philosophical Magazine 9, pp. 944–963, magnetism and atomic structure, London, Methuen,1926. Magnetism and matter, London, Methuen,1934, collective electron ferromagnetism in metals and alloys, Journal de physique et le radium 12, pp. 372–388
31.
Double-exchange mechanism
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The double-exchange mechanism is a type of a magnetic exchange that may arise between ions in different oxidation states. For example, consider the 180 degree interaction of Mn-O-Mn in which the Mn eg orbitals are directly interacting with the O 2p orbitals, and one of the Mn ions has more electrons than the other. In the ground state, electrons on each Mn ion are aligned according to the Hunds rule, If O gives up its spin-up electron to Mn +4, at the end of the process, an electron has moved between the neighboring metal ions, retaining its spin. The ability to hop reduces the kinetic energy, hence the overall energy saving can lead to ferromagnetic alignment of neighboring ions. This model is similar to superexchange. Exchange Mechanisms in E. Pavarini, E. Koch, F. Anders, and M. Jarrell, Correlated Electrons, From Models to Materials, Jülich 2012, ISBN 978-3-89336-796-2
32.
Multipolar exchange interaction
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Due to the strong spin-orbit coupling, multipoles are automatically introduced to the systems when the total angular momentum quantum number J is larger than 1/2. If those multipoles are coupled by some exchange mechanisms, those multipoles could tend to have some ordering as conventional spin 1/2 Heisenberg problem, then any quantum operators can be represented using the basis set as a matrix with dimension. Therefore, one can define 2 matrices to completely expand any quantum operator in this Hilbert space, any quantum operator defined in this Hilbert can be expended by operators. In the following, lets call these matrices as a basis to distinguish the eigen basis of quantum states. More speifically the above super basis can be called transition super basis because it describes the transition between states | i ⟩ and | j ⟩, in fact, this is not the only super basis that does the trick. If we extend the problem to J =1, we will need 9 matrices to form a super basis, for transition super basis, we have. For cubic super basis, we have, for spherical super basis, we have. The example tells us, for a J -multiplet problem, one will need all rank 0 ∼2 J tensor operators to form a super basis. Therefore, for a J =1 system, its density matrix must have quadrupole components. g, apparently, one can make linear combination of these operators to form a new super basis that have different symmetries. Using the addition theorem of tensor operators, the product of a rank n tensor, therefore, a high rank tensor can be expressed as the product of low rank tensors. This convention is useful to interpret the high rank multipolar exchange terms as a process of dipoles. Hence not only inter-site-exchange but also intra-site-exchange terms appear, if J is even larger, one can expect more complicated intra-site-exchange terms would appear. However, one has to note that it is not a perturbation expansion, the high rank terms are not necessarily smaller than low rank terms. In many systems, high rank terms are more important than low rank terms, there are four major mechanisms to induce exchange interactions between two magnetic moments in a system, 1). One can immediately find if K is restricted to 1 only, an important feature of the multipolar exchange Hamiltonian is its anisotropy. The value of coupling constant C K i K j Q i Q j is usually sensitive to the relative angle between two multipoles. This is one of the reasons that most multipolar orderings tend to be non-colinear. Taking a T y z moment as an example, if one flips the z-axis by making a π rotation toward the y-axis, it just changes nothing
33.
David J. Griffiths
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David Jeffrey Griffiths is a U. S. physicist and educator. He worked at Reed College from 1978 through 2009, becoming the Howard Vollum Professor of Science before his retirement and he is not to be confused with the late physicist David J. Griffiths of Oregon State University. Griffiths is a graduate of The Putney School and was trained at Harvard University and his doctoral work on theoretical particle physics was supervised by Sidney Coleman. He was also the recipient of the 1997 Robert A. Millikan award reserved for those who have made outstanding contributions to physics education. In 2009 he was named a Fellow of the American Physical Society, the most recent edition of each book is generally regarded as a standard undergraduate text. Griffithss web page Lecture, The charge distribution on a conductor, David Griffiths at the Mathematics Genealogy Project David Griffiths Lecture, Techfest 2012, IIT Bombay - YouTube
34.
Georgia State University
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Georgia State University is a public research university in downtown Atlanta, Georgia, United States. Founded in 1913, it is one of the University System of Georgias four research universities, Georgia State University offers more than 250 undergraduate and graduate degree programs spread across eight academic colleges with around 3,500 faculty members. It is accredited by the Southern Association of Colleges and Schools, approximately 27% of the student population is considered part-time while 73% of the population is considered full-time. The university is one of only four Georgia universities classified as a Research University/Very High Activity, the university has a full-time faculty count of 1,142, with 69 percent of those faculty members either tenured or on tenure track. GSU has two libraries, University library and Law library, which hold over 4.3 million volumes combined, the university has an economic impact on the Atlanta economy of more than $1.4 billion annually. Initially intended as a school, Georgia State University was established in 1913 as the Georgia School of Technologys Evening School of Commerce. During this time, the school was divided into two divisions, Georgia Evening College, and Atlanta Junior College, in September 1947, the school became affiliated with the University of Georgia and was named the Atlanta Division of the University of Georgia. The school was removed from the University of Georgia in 1955. In 1961, other programs at the school had grown enough that the name was shortened to Georgia State College. It became Georgia State University in 1969, in 1995, the Georgia Board of Regents accorded Georgia State research university status, joining the Georgia Institute of Technology, the University of Georgia, and Augusta University. The first African-American student enrolled at Georgia State in 1962, a year after the integration of the University of Georgia and Georgia Tech. Annette Lucille Hall was a Lithonia social studies teacher who enrolled in the course of the Institute on Americanism and Communism, a course required for all Georgia social studies teachers. The Peachtree Road Race, was started in 1970 by Georgia State cross country coach and dean of men Tim Singleton, the second year, he created the first valuable collectible T-shirt. Over its 100-plus year history, Georgia States growth has required the acquisition and construction of space to suit its needs. In addition, a plaza and walkway system was constructed to connect these buildings with each other over Decatur Street. Georgia States first move into the Fairlie-Poplar district was the acquisition and renovation of the Standard Building, the Haas-Howell Building, and the Rialto Theater in 1996. The Standard and Haas-Howell buildings house classrooms, offices, and practice spaces for the School of Music, and the Rialto is home to GSUs Jazz Studies program and an 833-seat theater. In 1998, the Student Center was expanded toward Gilmer Street and provided a new 400-seat auditorium and space for exhibitions, a new Student Recreation Center opened on the corner of Piedmont Avenue and Gilmer Street in 2001
35.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker