In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. These particles obey the Pauli exclusion principle. Fermions include all quarks and leptons, as well as all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons. 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 spin-statistics theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions. In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is 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 particular quantum state at any given time. If multiple fermions have the same spatial probability distribution at least one property of each fermion, such as its spin, must be different.
Fermions are associated with matter, whereas bosons are force carrier particles, although in the current state of particle physics the distinction between the two concepts is unclear. Weakly interacting fermions can 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 name fermion was coined by English theoretical physicist Paul Dirac from the surname of Italian physicist Enrico Fermi. The Standard Model recognizes two types of elementary fermions: leptons. In all, the model distinguishes 24 different fermions. There are six quarks, six leptons, along with the corresponding antiparticle of each of these. Mathematically, fermions come in three types: Weyl fermions, Dirac fermions, 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 fermions depending on their constituents. More because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion, it will have half-integer spin. Examples include the following: A baryon, such as the proton or neutron, contains three fermionic quarks and thus it is a fermion; the nucleus of a carbon-13 atom is therefore a fermion. The atom helium-3 is made of two protons, one neutron, two electrons, therefore it is a fermion; the number of bosons within a composite particle 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 composite 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. This is the origin of superconductivity and the superfluidity of helium-3: in superconducting materials, electrons interact through the exchange of phonons, forming Cooper pairs, while in helium-3, Cooper pairs are formed via spin fluctuations; the quasiparticles of the fractional quantum Hall effect are known as composite fermions, which are electrons with an number of quantized vortices attached to them. In a quantum field theory, there can be field configurations of bosons which are topologically twisted; these are coherent states which behave like a particle, they can be fermionic if all the constituent particles are bosons. This was discovered by Tony Skyrme in the early 1960s, so fermions made of bosons are named skyrmions after him. Skyrme's original example involved fields which take values on a three-dimensional sphere, the original nonlinear sigma model which describes the large distance behavior of pions. In Skyrme's model, reproduced in the large N or string approximation to quantum chromodynamics, the proton and neutron are fermionic topological solitons of the pion field.
Whereas Skyrme's example involved pion physics, there is a much more familiar example in quantum electrodynamics with a magnetic monopole. A bosonic monopole with the smallest possible magnetic charge and a bosonic version of the electron will form a fermionic dyon; the analogy between the Skyrme field and the Higgs field of the electroweak sector has been used to postulate that all fermions are skyrmions. This could explain why all known fermions have baryon or lepton quantum numbers and provide a physical mechanism for the Pauli exclusion principle
Wolfgang Ernst Pauli was an Austrian-born Swiss and American theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or Pauli principle"; the discovery involved spin theory, the basis of a theory of the structure of matter. Pauli was born in Vienna to his wife Bertha Camilla Schütz. Pauli's middle name was given in honor of physicist Ernst Mach. Pauli's paternal grandparents were from prominent Jewish families of Prague. Pauli's father converted from Judaism to Roman Catholicism shortly before his marriage in 1899. Pauli's mother, Bertha Schütz, was raised in her own mother's Roman Catholic religion. Pauli was raised as a Roman Catholic, although he and his parents left the Church, he is considered to have been a mystic. Pauli attended the Döblinger-Gymnasium in Vienna, graduating with distinction in 1918.
Only two months after graduation, he published his first paper, on Albert Einstein's theory of general relativity. He attended the Ludwig-Maximilians University in Munich, working under Arnold Sommerfeld, where he received his PhD in July 1921 for his thesis on the quantum theory of ionized diatomic hydrogen. Sommerfeld asked Pauli to review the theory of relativity for the Encyklopädie der mathematischen Wissenschaften. Two months after receiving his doctorate, Pauli completed the article, it was praised by Einstein. Pauli spent a year at the University of Göttingen as the assistant to Max Born, the following year at the Institute for Theoretical Physics in Copenhagen, which became the Niels Bohr Institute in 1965. From 1923 to 1928, he was a lecturer at the University of Hamburg. During this period, Pauli was instrumental in the development of the modern theory of quantum mechanics. In particular, he formulated the theory of nonrelativistic spin. In 1928, he was appointed Professor of Theoretical Physics at ETH Zurich in Switzerland where he made significant scientific progress.
He held visiting professorships at the University of Michigan in 1931, the Institute for Advanced Study in Princeton in 1935. He was awarded the Lorentz Medal in 1931. At the end of 1930, shortly after his postulation of the neutrino and following his divorce and the suicide of his mother, Pauli experienced a personal crisis, he consulted psychotherapist Carl Jung who, like Pauli, lived near Zurich. Jung began interpreting Pauli's archetypal dreams, Pauli became one of the depth psychologist's best students, he soon began to criticize the epistemology of Jung's theory scientifically, this contributed to a certain clarification of the latter's thoughts about the concept of synchronicity. A great many of these discussions are documented in the Pauli/Jung letters, today published as Atom and Archetype. Jung's elaborate analysis of more than 400 of Pauli's dreams is documented in Psychology and Alchemy; the German annexation of Austria in 1938 made him a German citizen, which became a problem for him in 1939 after the outbreak of World War II.
In 1940, he tried in vain to obtain Swiss citizenship, which would have allowed him to remain at the ETH. Pauli moved to the United States in 1940, where he was employed as a professor of theoretical physics at the Institute for Advanced Study. In 1946, after the war, he became a naturalized citizen of the United States and subsequently returned to Zurich, where he remained for the rest of his life. In 1949, he was granted Swiss citizenship. In 1958, Pauli was awarded the Max Planck medal. In that same year, he fell ill with pancreatic cancer; when his last assistant, Charles Enz, visited him at the Rotkreuz hospital in Zurich, Pauli asked him: "Did you see the room number?" It was number 137. Throughout his life, Pauli had been preoccupied with the question of why the fine structure constant, a dimensionless fundamental constant, has a value nearly equal to 1/137. Pauli died in that room on 15 December 1958. Pauli made many important contributions as a physicist in the field of quantum mechanics.
He published papers, preferring lengthy correspondences with colleagues such as Niels Bohr and Werner Heisenberg, with whom he had close friendships. Many of his ideas and results were never published and appeared only in his letters, which were copied and circulated by their recipients. Pauli proposed in 1924 a new quantum degree of freedom with two possible values, in order to resolve inconsistencies between observed molecular spectra and the developing theory of quantum mechanics, he formulated the Pauli exclusion principle his most important work, which stated that no two electrons could exist in the same quantum state, identified by four quantum numbers including his new two-valued degree of freedom. The idea of spin originated with Ralph Kronig. George Uhlenbeck and Samuel Goudsmit one year identified Pauli's new degree of freedom as electron spin, a discovery in which Pauli for a long time wrongly refused to believe. In 1926, shortly after Heisenberg published the matrix theory of modern quantum mechanics, Pauli used it to derive the observed spectrum of the hydrogen atom.
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The Schrödinger equation is a linear partial differential equation that describes the wave function or state function of a quantum-mechanical system. It is a key result in quantum mechanics, its discovery was a significant landmark in the development of the subject; the equation is named after Erwin Schrödinger, who derived the equation in 1925, published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. In classical mechanics, Newton's second law is used to make a mathematical prediction as to what path a given physical system will take over time following a set of known initial conditions. Solving this equation gives the position and the momentum of the physical system as a function of the external force F on the system; those two parameters are sufficient to describe its state at each time instant. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation; the concept of a wave function is a fundamental postulate of quantum mechanics.
Using these postulates, Schrödinger's equation can be derived from the fact that the time-evolution operator must be unitary, must therefore be generated by the exponential of a self-adjoint operator, the quantum Hamiltonian. This derivation is explained below. In the Copenhagen interpretation of quantum mechanics, the wave function is the most complete description that can be given of a physical system. Solutions to Schrödinger's equation describe not only molecular and subatomic systems, but macroscopic systems even the whole universe. Schrödinger's equation is central to all applications of quantum mechanics including quantum field theory which combines special relativity with quantum mechanics. Theories of quantum gravity, such as string theory do not modify Schrödinger's equation; the Schrödinger equation is not the only way to study quantum mechanical systems and make predictions. The other formulations of quantum mechanics include matrix mechanics, introduced by Werner Heisenberg, the path integral formulation, developed chiefly by Richard Feynman.
Paul Dirac incorporated the Schrödinger equation into a single formulation. The form of the Schrödinger equation depends on the physical situation; the most general form is the time-dependent Schrödinger equation, which gives a description of a system evolving with time: where i is the imaginary unit, ℏ = h 2 π is the reduced Planck constant, Ψ is the state vector of the quantum system, t is time, H ^ is the Hamiltonian operator. The position-space wave function of the quantum system is nothing but the components in the expansion of the state vector in terms of the position eigenvector | r ⟩, it is a scalar function, expressed as Ψ = ⟨ r | Ψ ⟩. The momentum-space wave function can be defined as Ψ ~ = ⟨ p | Ψ ⟩, where | p ⟩ is the momentum eigenvector; the most famous example is the nonrelativistic Schrödinger equation for the wave function in position space Ψ of a single particle subject to a potential V, such as that due to an electric field. Where m is the particle's mass, ∇ 2 is the Laplacian.
This is a diffusion equation, but unlike the heat equation, this one is a wave equation given the imaginary unit present in the transient term. The term "Schrödinger equation" can refer to both the general equation, or the specific nonrelativistic version; the general equation is indeed quite general, used throughout quantum mechanics, for everything from the Dirac equation to quantum field theory, by plugging in diverse expressions for the Hamiltonian. The specific nonrelativistic version is a classical approximation to reality and yields accurate results in many situations, but only to a certain extent. To apply the Schrödinger equation, write down the Hamiltonian for the system, accounting for the kinetic and potential energies of the particles constituting the system insert it into the Schrödinger equation; the resulting partial differential equation is solved for the wave function, which contains information about the system. The time-dependent Schrödinger equation described above predicts that wave functions can form standing waves, called stationary states.
These states are important as their individual study simplifies the task of solving the time-dependent Schrödinger equation for any state. Stationary states can be described by a simpler form of the Schrödinger equation, the time-independe
The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current, permanent magnets, elementary particles, various molecules, many astronomical objects. More the term magnetic moment refers to a system's magnetic dipole moment, the component of the magnetic moment that can be represented by an equivalent magnetic dipole: a magnetic north and south pole separated by a small distance; the magnetic dipole component is sufficient for large enough distances. Higher order terms may be needed in addition to the dipole moment for extended objects; the magnetic dipole moment of an object is defined in terms of the torque that object experiences in a given magnetic field. The same applied magnetic field creates larger torques on objects with larger magnetic moments; the strength of this torque depends not only on the magnitude of the magnetic moment but on its orientation relative to the direction of the magnetic field.
The magnetic moment may be considered, therefore. The direction of the magnetic moment points from the south to north pole of the magnet; the magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, decreases as the inverse cube of the distance from the object; the magnetic moment can be defined as a vector relating the aligning torque on the object from an externally applied magnetic field to the field vector itself. The relationship is given by: τ = m × B where τ is the torque acting on the dipole, B is the external magnetic field, m is the magnetic moment; this definition is based on how one could, in principle, measure the magnetic moment of an unknown sample. For a current loop, this definition leads to the magnitude of the magnetic dipole moment equaling the product of the current times the area of the loop. Further, this definition allows the calculation of the expected magnetic moment for any known macroscopic current distribution.
An alternative definition is useful for thermodynamics calculations of the magnetic moment. In this definition, the magnetic dipole moment of a system is the negative gradient of its intrinsic energy, with respect to external magnetic field: m = − x ^ ∂ U i n t ∂ B x − y ^ ∂ U i n t ∂ B y − z ^ ∂ U i n t ∂ B z. Generically, the intrinsic energy includes the self-field energy of the system plus the energy of the internal workings of the system. For example, for a hydrogen atom in a 2p state in an external field, the self-field energy is negligible, so the internal energy is the eigenenergy of the 2p state, which includes Coulomb potential energy and the kinetic energy of the electron; the interaction-field energy between the internal dipoles and external fields is not part of this internal energy. The unit for magnetic moment in International System of Units base units is A⋅m2, where A is ampere and m is meter; this unit has equivalents in other SI derived units including: A ⋅ m 2 = N ⋅ m T = J T, where N is newton, T is tesla, J is joule.
Although torque and energy are dimensionally equivalent, torques are never expressed in units of energy. In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU, EMU. Among these, there are two alternative units of magnetic dipole moment: 1 statA ⋅ cm 2 = 3.33564095 × 10 − 14 A ⋅ m 2 1 erg G = 10 − 3 A ⋅ m 2,where statA is statamperes, cm is centimeters, erg is ergs, G is gauss. The ratio of these two non-equivalent CGS units is equal to the speed of light in free space, expressed in cm⋅s−1. All formula
The Planck constant is a physical constant, the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant; the Planck constant is of fundamental importance in quantum mechanics, in metrology it is the basis for the definition of the kilogram. At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by had been measured, diverged at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum, he assumed that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, that constant is named in his honor.
In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave, it was called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". Since energy and mass are equivalent, the Planck constant relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram, that had defined the kilogram since 1889; the new definition was unanimously approved at the General Conference on Weights and Measures on 16 November 2018 as part of the 2019 redefinition of SI base units. For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.62607015×10−34 J⋅s exactly.
The kilogram was the last SI base unit to be re-defined by a fundamental physical property to replace a physical artefact. In the last years of the 19th century, Max Planck was investigating the problem of black-body radiation first posed by Kirchhoff some 40 years earlier; every physical body continuously emits electromagnetic radiation. At low frequencies, Planck's law tends to the Rayleigh–Jeans law, while in the limit of high frequencies it tends to the Wien approximation but there was no overall expression or explanation for the shape of the observed emission spectrum. Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency, he examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, was able to derive an approximate mathematical function for black-body spectrum. To create Planck's law, which predicts blackbody emissions by fitting the observed curves, he multiplied the classical expression by a complex factor that involves a constant, h, in both the numerator and the denominator, which subsequently became known as the Planck Constant.
The spectral radiance of a body, Bν, describes the amount of energy it emits at different radiation frequencies. It is the power emitted per unit area of the body, per unit solid angle of emission, per unit frequency. Planck showed that the spectral radiance of a body for frequency ν at absolute temperature T is given by B ν = 2 h ν 3 c 2 1 e h ν k B T − 1 where kB is the Boltzmann constant, h is the Planck constant, c is the speed of light in the medium, whether material or vacuum; the spectral radiance can be expressed per unit wavelength λ instead of per unit frequency. In this case, it is given by B λ = 2 h c 2 λ 5 1 e h c λ k B T − 1. Showing how radiated energy emitted at shorter wavelengths increases more with temperature than energy emitted at longer wavelengths; the law may be expressed in other terms, such as the number of photons emitted at a certain wavelength, or the energy density in a volume of radiation. The SI units of Bν are W·sr−1·m−2·Hz−1, while those of Bλ are W·sr−1·m−3.
Planck soon realized. There were several different solutions, each of which gave a different value for the entropy of the oscillators. To save his theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as "an act of despair … I was ready to sacrifice any of my previous convictions about physics." One of his new boundary conditions was to interpret UN [the vibrational energy
Otto Stern was the pen name of German women's rights activist Louise Otto-Peters. Otto Stern was Nobel laureate in physics, he was the second most nominated person for a Nobel Prize with 82 nominations in the years 1925–1945 winning in 1943. Stern was born into a Jewish family in Sohrau in Upper Silesia, the German Empire's Kingdom of Prussia, he studied in Freiburg im Breisgau and Breslau, now Wrocław in Lower Silesia. Stern completed his studies at the University of Breslau in 1912 with a doctoral dissertation in physical chemistry under supervision of Otto Sackur on the kinetic theory of osmotic pressure in concentrated solutions, he followed Albert Einstein to Charles University in Prague and in 1913 to ETH Zurich. Stern served in World War I doing meteorological work on the Russian front while still continuing his studies and in 1915 received his Habilitation at the University of Frankfurt. In 1921 he became a professor at the University of Rostock which he left in 1923 to become director of the newly founded Institut für Physikalische Chemie at the University of Hamburg.
After resigning from his post at the University of Hamburg in 1933 because of the Nazis' Machtergreifung, he became professor of physics at the Carnegie Institute of Technology. During the 1930s, he was a visiting professor at the University of Berkeley; as an experimental physicist Stern contributed to the discovery of spin quantization in the Stern–Gerlach experiment with Walther Gerlach in February 1922 at the Physikalischer Verein in Frankfurt am Main. He was awarded the 1943 Nobel Prize in Physics, the first to be awarded since 1939, he was the sole recipient in Physics that year, the award citation omitted mention of the Stern–Gerlach experiment, as Gerlach had remained active in Nazi-led Germany. After Stern retired from the Carnegie Institute of Technology, he moved to California, he was a regular visitor to the Physics colloquium at UC Berkeley. He died of a heart attack in Berkeley on 17 August 1969; the Stern-Gerlach-Medaille of the Deutsche Physikalische Gesellschaft awarded for excellence in experimental physics is named after him and Gerlach.
His niece was the crystallographer Lieselotte Templeton. List of German inventors and discoverers Horst Schmidt-Böcking and Karin Reich: Otto Stern. Physiker Querdenker, Nobelpreisträger. Societäts-Verlag, Frankfurt am Main 2011, ISBN 978-3-942921-23-7. J. P. Toennies, H. Schmidt-Böcking, B. Friedrich3, J. C. A. Lower. Otto Stern: The founding father of experimental atomic physics. Annalen der Physik, 523, 1045–1070. ArXiv:1109.4864 National Academy of Sciences - Otto Stern Otto Stern, Nobel Luminaries - Jewish Nobel Prize Winners, on the Beit Hatfutsot-The Museum of the Jewish People Website. Otto Stern's biography at nobelprize.org Stern's publication on his molecular beam method Otto Stern School Frankfurt am Main, Germany