Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, describes nature at ordinary scale. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large scale. Quantum mechanics differs from classical physics in that energy, angular momentum and other quantities of a bound system are restricted to discrete values. Quantum mechanics arose from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, from the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others; the modern 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 and other physical properties of a particle. Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, the laser, the transistor and semiconductors such as the microprocessor and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA. Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations. In 1803, Thomas Young, an English polymath, performed the famous double-slit experiment that he described in a paper titled On the nature of light and colours.
This experiment played a major role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays; these studies were followed by the 1859 statement of the black-body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system can be discrete, the 1900 quantum hypothesis of Max Planck. Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, known as Wien's law in his honor. Ludwig Boltzmann independently arrived at this result by considerations of Maxwell's equations. However, it underestimated the radiance at low frequencies. Planck corrected this model using Boltzmann's statistical interpretation of thermodynamics and proposed what is now called Planck's law, which led to the development of quantum mechanics. Following Max Planck's solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect.
Around 1900–1910, the atomic theory and the corpuscular theory of light first came to be accepted as scientific fact. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, Pieter Zeeman, each of whom has a quantum effect named after him. Robert Andrews Millikan studied the photoelectric effect experimentally, Albert Einstein developed a theory for it. At the same time, Ernest Rutherford experimentally discovered the nuclear model of the atom, for which Niels Bohr developed his theory of the atomic structure, confirmed by the experiments of Henry Moseley. In 1913, Peter Debye extended Niels Bohr's theory of atomic structure, introducing elliptical orbits, a concept introduced by Arnold Sommerfeld; 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 Planck's constant. Planck cautiously insisted that this was an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself.
In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizable discovery. However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material, he won the 1921 Nobel Prize in Physics for this work. Einstein further developed this idea to show that an electromagnetic wave such as light could be described as a particle, with a discrete quantum of energy, dependent on its frequency; the foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wi
Karl Schwarzschild was a German physicist and astronomer. He was the father of astrophysicist Martin Schwarzschild. Schwarzschild provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he accomplished in 1915, the same year that Einstein first introduced general relativity; the Schwarzschild solution, which makes use of Schwarzschild coordinates and the Schwarzschild metric, leads to a derivation of the Schwarzschild radius, the size of the event horizon of a non-rotating black hole. Schwarzschild accomplished this while serving in the German army during World War I, he died the following year from the autoimmune disease pemphigus, which he developed while at the Russian front. Various forms of the disease affect people of Ashkenazi Jewish origin. Asteroid 837 Schwarzschilda is named in his honour, as is the large crater Schwarzschild, on the far side of the Moon. Schwarzschild was born in Frankfurt am Main to Jewish parents.
His father was active in the business community of the city, the family had ancestors in the city dating back to the sixteenth century. Karl attended a Jewish primary school until 11 years of age, he was something of a child prodigy, having two papers on binary orbits published before he was sixteen. He studied at Strasbourg and Munich, obtaining his doctorate in 1896 for a work on Henri Poincaré's theories. From 1897, he worked as assistant at the Kuffner Observatory in Vienna. From 1901 until 1909 he was a professor at the prestigious institute at Göttingen, where he had the opportunity to work with some significant figures, including David Hilbert and Hermann Minkowski. Schwarzschild became the director of the observatory in Göttingen, he married Else Rosenbach, the daughter of a professor of surgery at Göttingen, in 1909, that year moved to Potsdam, where he took up the post of director of the Astrophysical Observatory. This was the most prestigious post available for an astronomer in Germany.
He and Else had three children, Agathe and Alfred. From 1912, Schwarzschild was a member of the Prussian Academy of Sciences. At the outbreak of World War I in 1914 he joined the German army, despite being over 40 years old, he served on both the eastern fronts, rising to the rank of lieutenant in the artillery. While serving on the front in Russia in 1915, he began to suffer from a rare and painful autoimmune skin disease called pemphigus, he managed to write three outstanding papers, two on the theory of relativity and one on quantum theory. His papers on relativity produced the first exact solutions to the Einstein field equations, a minor modification of these results gives the well-known solution that now bears his name — the Schwarzschild metric. Schwarzschild's struggle with pemphigus may have led to his death on May 11, 1916. Thousands of dissertations and books have since been devoted to the study of Schwarzschild's solutions to the Einstein field equations. However, although Schwarzschild's best known work lies in the area of general relativity, his research interests were broad, including work in celestial mechanics, observational stellar photometry, quantum mechanics, instrumental astronomy, stellar structure, stellar statistics, Halley's comet, spectroscopy.
Some of his particular achievements include measurements of variable stars, using photography, the improvement of optical systems, through the perturbative investigation of geometrical aberrations. While at Vienna in 1897, Schwarzschild developed a formula, now known as the Schwarzschild law, to calculate the optical density of photographic material, it involved an exponent now known as the Schwarzschild exponent, the p in the formula: i = f. This formula was important for enabling more accurate photographic measurements of the intensities of faint astronomical sources. According to Wolfgang Pauli, Schwarzschild is the first to introduce the correct Lagrangian formalism of the electromagnetic field as S = ∫ d V + ∫ ρ d V where E →, H → are the electric and magnetic field, A → is the vector potential and ϕ is the electric potential, he introduced a field free variational formulation of electrodynamics based only on the world line of particles as S = ∑ i m i ∫ C i d s i + 1 2 ∑
Johannes Stark was a German physicist, awarded the Nobel Prize in Physics in 1919 "for his discovery of the Doppler effect in canal rays and the splitting of spectral lines in electric fields". This phenomenon is known as the Stark effect. Stark received his Ph. D. in physics from the University of Munich in 1897 under the supervision of Eugen von Lommel, served as Lommel's assistant until his appointment as a lecturer at the University of Göttingen in 1900. He was an extraordinary professor at the University of Hannover from 1906 until he became a professor at RWTH Aachen University in 1909. In 1917, he became professor at the University of Greifswald, he worked at the University of Würzburg from 1920 to 1922. A supporter of Adolf Hitler from 1924, Stark was one of the main figures, along with fellow Nobel laureate Philipp Lenard, in the anti-Semitic Deutsche Physik movement, which sought to remove Jewish scientists from German physics, he was appointed head of the German Research Foundation in 1933 and was president of the Reich Physical-Technical Institute from 1933 to 1939.
In 1947, he was found guilty as a "Major Offender" by a denazification court. Born in Schickenhof, Kingdom of Bavaria, Stark was educated at the Bayreuth Gymnasium and in Regensburg, his collegiate education began at the University of Munich, where he studied physics, mathematics and crystallography. His tenure at that college began in 1894. Stark worked in various positions at the Physics Institute of his alma mater until 1900, when he became an unsalaried lecturer at the University of Göttingen. An extraordinary professor at Hanover by 1906, in 1908 he became professor at the RWTH Aachen University, he worked and researched at physics departments of several universities, including the University of Greifswald, until 1922. In 1919, he won the Nobel Prize in Physics for his "discovery of the Doppler effect in canal rays and the splitting of spectral lines in electric fields". From 1933 until his retirement in 1939, Stark was elected President of the Physikalisch-Technische Reichsanstalt, while President of the Deutsche Forschungsgemeinschaft.
It was Stark who, as the editor of Jahrbuch der Radioaktivität und Elektronik, asked in 1907 still rather unknown, Albert Einstein to write a review article on the principle of relativity. Stark seemed impressed by relativity and Einstein's earlier work when he quoted "the principle of relativity formulated by H. A. Lorentz and A. Einstein" and "Planck's relationship M0 = E0/c2" in his 1907 paper in Physikalische Zeitschrift, where he used the equation e0 = m0c2 to calculate an "elementary quantum of energy", i.e. the amount of energy related to the mass of an electron at rest. While working on his article, Einstein began a line of thought that would lead to his generalized theory of relativity, which in turn became the start of Einstein's worldwide fame; this is ironic, given Stark's work as an anti-Einstein and anti-relativity propagandist in the Deutsche Physik movement. Stark published more than 300 papers regarding electricity and other such topics, he received various awards, including the Nobel Prize, the Baumgartner Prize of the Vienna Academy of Sciences, the Vahlbruch Prize of the Göttingen Academy of Sciences, the Matteucci Medal of the Rome Academy.
His best known contribution to the field of physics is the Stark effect, which he discovered in 1913. He married Luise Uepler, they had five children, his hobbies were the cultivation of forestry. He worked in his private laboratory on his country estate in Upper Bavaria after the war. There he studied the deflection of light in an electric field. From 1924 onwards, Stark supported Hitler. During the Nazi regime, Stark attempted to become the Führer of German physics through the Deutsche Physik movement against the "Jewish physics" of Albert Einstein and Werner Heisenberg. After Werner Heisenberg defended Albert Einstein's theory of relativity, Stark wrote an angry article in the SS newspaper Das Schwarze Korps, calling Heisenberg a "White Jew". On August 21, 1934, Stark wrote to physicist and fellow Nobel laureate Max von Laue to toe the party line or else; the letter was signed off with "Heil Hitler."In his 1934 book Nationalsozialismus und Wissenschaft Stark maintained that the priority of the scientist was to serve the nation—thus, the important fields of research were those that could help German arms production and industry.
He attacked theoretical physics as "Jewish" and stressed that scientific positions in Nazi Germany should only be held by pure-blooded Germans. Writing in the official SS magazine Das Schwarze Korps, Stark argued that if racial antisemitism was triumphant, it would only be a'partial victory' if'Jewish' ideas were not defeated: "‘we have to eradicate the Jewish spirit, whose blood can flow just as undisturbed today as before if its carriers hold beautiful Aryan passes". In 1947, following the defeat of Germany in World War II, Stark was classified as a "Major Offender" and received a sentence of four years' imprisonment by a denazification court. Die Entladung der Elektricität von galvanisch glühender Kohle in verdünntes Gas.. Leipzig, 1899 Der
In mechanical systems, resonance is a phenomenon that occurs when the frequency at which a force is periodically applied is equal or nearly equal to one of the natural frequencies of the system on which it acts. This causes the system to oscillate with larger amplitude than when the force is applied at other frequencies. Frequencies at which the response amplitude is a relative maximum are known as resonant frequencies or resonance frequencies of the system. Near resonant frequencies, small periodic forces have the ability to produce large amplitude oscillations, due to the storage of vibrational energy. In other systems, such as electrical or optical, phenomena occur which are described as resonance but depend on interaction between different aspects of the system, not on an external driver. For example, electrical resonance occurs in a circuit with capacitors and inductors because the collapsing magnetic field of the inductor generates an electric current in its windings that charges the capacitor, the discharging capacitor provides an electric current that builds the magnetic field in the inductor.
Once the circuit is charged, the oscillation is self-sustaining, there is no external periodic driving action. This is analogous to a mechanical pendulum, where mechanical energy is converted back and forth between kinetic and potential, both systems are forms of simple harmonic oscillators. In optical cavities, light confined in the cavity reflects forth multiple times; this produces standing waves, only certain patterns and frequencies of radiation are sustained, due to the effects of interference, while the others are suppressed by destructive interference. Once the light enters the cavity, the oscillation is self-sustaining, there is no external periodic driving action; some behavior is mistaken for resonance but instead is a form of self-oscillation, such as aeroelastic flutter, speed wobble, or Hunting oscillation. In these cases, the external energy source does not oscillate, but the components of the system interact with each other in a periodic fashion. Resonance occurs when a system is able to store and transfer energy between two or more different storage modes.
However, there are some losses from cycle to cycle, called damping. When damping is small, the resonant frequency is equal to the natural frequency of the system, a frequency of unforced vibrations; some systems have multiple, resonant frequencies. Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance, electron spin resonance and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency, or pick out specific frequencies from a complex vibration containing many frequencies; the term resonance originates from the field of acoustics observed in musical instruments, e.g. when strings started to vibrate and to produce sound without direct excitation by the player. A familiar example is a playground swing. Pushing a person in a swing in time with the natural interval of the swing makes the swing go higher and higher, while attempts to push the swing at a faster or slower tempo produce smaller arcs.
This is because the energy the swing absorbs is maximized when the pushes match the swing's natural oscillations. Resonance occurs in nature, is exploited in many manmade devices, it is the mechanism by which all sinusoidal waves and vibrations are generated. Many sounds we hear, such as when hard objects of metal, glass, or wood are struck, are caused by brief resonant vibrations in the object. Light and other short wavelength electromagnetic radiation is produced by resonance on an atomic scale, such as electrons in atoms. Other examples of resonance: Timekeeping mechanisms of modern clocks and watches, e.g. the balance wheel in a mechanical watch and the quartz crystal in a quartz watch Tidal resonance of the Bay of Fundy Acoustic resonances of musical instruments and the human vocal tract Shattering of a crystal wineglass when exposed to a musical tone of the right pitch Friction idiophones, such as making a glass object vibrate by rubbing around its rim with a fingertip Electrical resonance of tuned circuits in radios and TVs that allow radio frequencies to be selectively received Creation of coherent light by optical resonance in a laser cavity Orbital resonance as exemplified by some moons of the solar system's gas giants Material resonances in atomic scale are the basis of several spectroscopic techniques that are used in condensed matter physics Electron spin resonance Mössbauer effect Nuclear magnetic resonance The visible, rhythmic twisting that resulted in the 1940 collapse of "Galloping Gertie", the original Tacoma Narrows Bridge, is mistakenly characterized as an example of resonance phenomenon in certain textbooks.
The catastrophic vibrations that destroyed the bridge were not due to simple mechanical resonance, but to a more complicated interaction between the bridge and the winds passing through it—a phenomenon known as aeroelastic flutter, a kind of "self-sustaining vibration" as referred to in the nonlinear theory of vibrations. Robert H. Scanlan, father of bridge aerodynamics, has written an article about this misunderstanding; the rocket engines for the International Space Station are controlled by an autopilot. Ordinarily, uploaded parameters for controlling the engine control system for the Zvezda modu
A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. Magnetic fields are observed from subatomic particles to galaxies. In everyday life, the effects of magnetic fields are seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field vary with location; as such, it is an example of a vector field. The term'magnetic field' is used for two distinct but related fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter. B, magnetic flux density, is measured in tesla, equivalent to newton per meter per ampere.
H and B differ in. In a vacuum, B and H are the same aside from units. Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated, are both components of the electromagnetic force, one of the four fundamental forces of nature. Magnetic fields are used throughout modern technology in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric generators; the interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect; the Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass. Although magnets and magnetism were studied much earlier, the research of magnetic fields began in 1269 when French scholar Petrus Peregrinus de Maricourt mapped out the magnetic field on the surface of a spherical magnet using iron needles.
Noting that the resulting field lines crossed at two points he named those points'poles' in analogy to Earth's poles. He clearly articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them. Three centuries William Gilbert of Colchester replicated Petrus Peregrinus' work and was the first to state explicitly that Earth is a magnet. Published in 1600, Gilbert's work, De Magnete, helped to establish magnetism as a science. In 1750, John Michell stated that magnetic poles attract and repel in accordance with an inverse square law. Charles-Augustin de Coulomb experimentally verified this in 1785 and stated explicitly that the north and south poles cannot be separated. Building on this force between poles, Siméon Denis Poisson created the first successful model of the magnetic field, which he presented in 1824. In this model, a magnetic H-field is produced by'magnetic poles' and magnetism is due to small pairs of north/south magnetic poles. Three discoveries in 1820 challenged this foundation of magnetism, though.
Hans Christian Ørsted demonstrated that a current-carrying wire is surrounded by a circular magnetic field. André-Marie Ampère showed that parallel wires with currents attract one another if the currents are in the same direction and repel if they are in opposite directions. Jean-Baptiste Biot and Félix Savart announced empirical results about the forces that a current-carrying long, straight wire exerted on a small magnet, determining that the forces were inversely proportional to the perpendicular distance from the wire to the magnet. Laplace deduced, but did not publish, a law of force based on the differential action of a differential section of the wire, which became known as the Biot–Savart law. Extending these experiments, Ampère published his own successful model of magnetism in 1825. In it, he showed the equivalence of electrical currents to magnets and proposed that magnetism is due to perpetually flowing loops of current instead of the dipoles of magnetic charge in Poisson's model.
This has the additional benefit of explaining. Further, Ampère derived both Ampère's force law describing the force between two currents and Ampère's law, like the Biot–Savart law described the magnetic field generated by a steady current. In this work, Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism. In 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field, he described this phenomenon in. Franz Ernst Neumann proved that, for a moving conductor in a magnetic field, induction is a consequence of Ampère's force law. In the process, he introduced the magnetic vector potential, shown to be equivalent to the underlying mechanism proposed by Faraday. In 1850, Lord Kelvin known as William Thomson, distinguished between two magnetic fields now denoted H and B; the former applied to the latter to Ampère's model and induction. Further, he derived how H and B relate to each other
In physics and electronic engineering, an electron hole is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or crystal lattice the negative charge of the electrons is balanced by the positive charge of the atomic nuclei, the absence of an electron leaves a net positive charge at the hole's location. Holes are not particles, but rather quasiparticles. Holes in a metal or semiconductor crystal lattice can move through the lattice as electrons can, act to positively-charged particles, they play an important role in the operation of semiconductor devices such as transistors and integrated circuits. If an electron is excited into a higher state it leaves a hole in its old state; this meaning is used in Auger electron spectroscopy, in computational chemistry, to explain the low electron-electron scattering-rate in crystals. In crystals, electronic band structure calculations lead to an effective mass for the electrons, negative at the top of a band.
The negative mass is an unintuitive concept, in these situations a more familiar picture is found by considering a positive charge with a positive mass. In solid-state physics, an electron hole is the absence of an electron from a full valence band. A hole is a way to conceptualize the interactions of the electrons within a nearly full valence band of a crystal lattice, missing a small fraction of its electrons. In some ways, the behavior of a hole within a semiconductor crystal lattice is comparable to that of the bubble in a full bottle of water. Hole conduction in a valence band can be explained by the following analogy. Imagine a row of people seated in an auditorium, where there are no spare chairs. Someone in the middle of the row wants to leave, so he jumps over the back of the seat into another row, walks out; the empty row is analogous to the conduction band, the person walking out is analogous to a conduction electron. Now imagine someone else comes along and wants to sit down; the empty row has a poor view.
Instead, a person in the crowded row moves into the empty seat the first person left behind. The empty seat moves one spot closer to the person waiting to sit down; the next person follows, the next, et cetera. One could say. Once the empty seat reaches the edge, the new person can sit down. In the process everyone in the row has moved along. If those people were negatively charged, this movement would constitute conduction. If the seats themselves were positively charged only the vacant seat would be positive; this is a simple model of how hole conduction works. Instead of analyzing the movement of an empty state in the valence band as the movement of many separate electrons, a single equivalent imaginary particle called a "hole" is considered. In an applied electric field, the electrons move in one direction, corresponding to the hole moving in the other. If a hole associates itself with a neutral atom, that atom becomes positive. Therefore, the hole is taken to have positive charge of +e the opposite of the electron charge.
In reality, due to the uncertainty principle of quantum mechanics, combined with the energy levels available in the crystal, the hole is not localizable to a single position as described in the previous example. Rather, the positive charge which represents the hole spans an area in the crystal lattice covering many hundreds of unit cells; this is equivalent to being unable to tell. Conduction band electrons are delocalized; the analogy above is quite simplified, cannot explain why holes create an opposite effect to electrons in the Hall effect and Seebeck effect. A more precise and detailed explanation follows; the dispersion relation determines. A dispersion relation is the relationship between wavevector and energy in a band, part of the electronic band structure. In quantum mechanics, the electrons are waves, energy is the wave frequency. A localized electron is a wavepacket, the motion of an electron is given by the formula for the group velocity of a wave. An electric field affects an electron by shifting all the wavevectors in the wavepacket, the electron accelerates when its wave group velocity changes.
Therefore, the way an electron responds to forces is determined by its dispersion relation. An electron floating in space has the dispersion relation E=ℏ2k2/, where m is the electron mass and ℏ is reduced Planck constant. Near the bottom of the conduction band of a semiconductor, the dispersion relation is instead E=ℏ2k2/, so a conduction-band electron responds to forces as if it had the mass m*. Electrons near the top of the valence band behave; the dispersion relation near the top of the valence band is E=ℏ2k2/ with negative effective mass. So electrons near the top of the valence band behave; when a force pulls the electrons to the right, these electrons move left. This is due to the shape of the valence band, is unrelated to whether the band is full or empty. If you could somehow empty out the valence band and just put one electron near the valence band maximum, this electron would move the "wrong way" in response to forces. Po