Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron


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Publication Timeline. Most widely held works by Shigeji Fujita. Electrical conduction in graphene and nanotubes by Shigeji Fujita 17 editions published in in English and held by WorldCat member libraries worldwide This self-contained text teaches both advanced students and practicing applied physicists and engineers the relevant aspects from the bottom up.

An extensive list of references is given in the end of each chapter, with derivations and proofs of specific equations in the appendix, as well as a large number of exercise-type problems.


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Quantum statistical theory of superconductivity by Shigeji Fujita 27 editions published between and in English and held by WorldCat member libraries worldwide In this text, Shigeji Fujita and Salvador Godoy guide first and second-year graduate students through the essential aspects of superconductivity. The authors open with five preparatory chapters thoroughly reviewing a number of advanced physical concepts-such as free-electron model of a metal, theory of lattice vibrations, and Bloch electrons.

The remaining chapters deal with the theory of superconductivity-describing the basic properties of type I, type II compound, and high-Tc superconductors as well as treating quasi-particles using Heisenberg's equation of motion. The book includes step-by-step derivations of mathematical formulas, sample problems, and illustrations.

Quantum theory of conducting matter : Newtonian equations of motion for a Bloch electron by Shigeji Fujita 9 editions published between and in English and held by WorldCat member libraries worldwide Shows an important connection between the conduction electrons and the Fermi surface in an elementary manner. This title is intended for scientists, researchers and graduate-level students focused on experimentation in the fields of physics, chemistry, electrical engineering, and materials science. Introduction to non-equilibrium quantum statistical mechanics by Shigeji Fujita Book 29 editions published between and in English and Russian and held by WorldCat member libraries worldwide.

Johannes van der Waals Dutch worked on equations of state for gases and liquids.

Quantum Theory of Conducting Matter

Lord Rayleigh born John William Strutt British discovered argon; explained how light scattering is responsible for red color of sunset and blue color of sky. Antoine Henri Becquerel French discovered natural radioactivity. Albert A. Michelson German-born American devised an interferometer and used it to try to measure Earth's absolute motion; precisely measured speed of light. Hendrik Antoon Lorentz Dutch introduced Lorentz transformation equations of special relativity; advanced ideas of relativistic length contraction and relativistic mass increase; contributed to theory of electromagnetism.

Heike Kamerlingh-Onnes Dutch liquified helium; discovered superconductivity. Sir Joseph John Thomson British demonstrated existence of the electron. Max Planck German formulated the quantum theory; explained wavelength distribution of blackbody radiation. Pierre Curie French studied radioactivity with wife, Marie Curie; discovered piezoelectricity.

Sir William Henry Bragg British worked on x-ray spectrometry. Philipp von Lenard German studied cathode rays and the photoelectric effect. Wilhelm Wien German discovered laws governing radiation of heat. Pieter Zeeman Dutch discovered splitting of spectral lines in a strong magnetic field.

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Marie Curie Polish-born French discovered radioactivity of thorium; co-discovered radium and polonium. Charles Wilson British invented the cloud chamber. Jean Baptiste Perrin French experimentally proved that cathode rays were streams of negatively charged particles; experimentally confirmed the correctness of Einstein's theory of Brownian motion, and through his measurements obtained a new determination of Avogadro's number.

Lord Ernest Rutherford New Zealander theorized existence of the atomic nucleus based on results of the alpha-scattering experiment performed by Hans Geiger and Ernest Marsden; developed theory of Rutherford scattering scattering of spinless, pointlike particles from a Coulomb potential. Guglielmo Marconi Italian invented the first practical system of wireless telegraphy.

Johannes Stark German discovered splitting of spectral lines in a strong electric field. Charles Glover Barkla British discovered that every chemical element, when irradiated by x rays, can emit an x-ray spectrum of two line-groups, which he named the K-series and L-series, that are of fundamental importance to understanding atomic structure.

Albert Einstein German-born American explained Brownian motion and photoelectric effect; contributed to theory of atomic spectra; formulated theories of special and general relativity. Otto Hahn German discovered the fission of heavy nuclei. Max von Laue German discovered diffraction of x rays by crystals. Sir Owen Richardson British discovered the basic law of thermionic emission, now called the Richardson or Richardson-Dushman equation, which describes the emission of electrons from a heated conductor.

Clinton Joseph Davisson American co-discovered electron diffraction. Max Born German-born British contributed to creation of quantum mechanics; pioneer in the theory of crystals. Percy Williams Bridgman American invented an apparatus to produce extremely high pressures; made many discoveries in high-pressure physics. James Franck German experimentally confirmed that atomic energy states are quantized. Victor Franz Hess Austrian discovered cosmic radiation. Peter Debye Dutch-born German used methods of statistical mechanics to calculate equilibrium properties of solids; contributed to knowledge of molecular structure.

Niels Bohr Danish contributed to quantum theory and to theory of nuclear reactions and nuclear fission. Karl Manne Georg Siegbahn Swedish made important experimental contributions to the field of x-ray spectroscopy. Gustav Hertz German experimentally confirmed that atomic energy states are quantized. Sir Chandrasekhara Raman Indian studied light scattering and discovered the Raman effect.

Otto Stern German-born American contributed to development of the molecular beam method; discovered the magnetic moment of the proton. Frits Zernike Dutch invented the phase-contrast microscope, a type of microscope widely used for examining specimens such as biological cells and tissues. Sir William Lawrence Bragg British worked on crystal structure and x rays. Walther Bothe German devised a coincidence counter for studying cosmic rays; demonstrated validity of energy-momentum conservation at the atomic scale.

Sir James Chadwick British discovered the neutron. Sir Edward Appleton English discovered the layer of the Earth's atmosphere, called the Appleton layer, which is the part of the ionosphere having the highest concentration of free electrons and is the most useful for radio transmission. Prince Louis-Victor de Broglie French predicted wave properties of the electron.

Arthur Compton American discovered the increase in wavelength of x rays when scattered by an electron. Sir George Paget Thomson British co-discovered electron diffraction. Harold Clayton Urey American discovered deuterium. Pjotr Leonidovich Kapitsa Soviet heralded a new era of low-temperature physics by inventing a device for producing liquid helium without previous cooling with liquid hydrogen; demonstrated that Helium II is a quantum superfluid. Igor Y. Robert S. Mulliken American introduced the theoretical concept of the molecular orbital, which led to a new understanding of the chemical bond and the electronic structure of molecules.

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Lord Patrick Maynard Stuart Blackett British developed an automatic Wilson cloud chamber; discovered electron-positron pair production in cosmic rays. Sir John Cockcroft British co-invented the first particle accelerator. Isador Isaac Rabi Austrian-born American developed the resonance technique for measuring the magnetic properties of atomic nuclei.

Dennis Gabor Hungarian invented and developed the holographic method whereby it is possible to record and display a three-dimensional display of an object. Wolfgang Pauli Austrian-born American discovered the exclusion principle; suggested the existence of the neutrino. Enrico Fermi Italian-born American performed experiments leading to first self-sustaining nuclear chain reaction; developed a theory of beta decay that introduced the weak interaction; derived the statistical properties of gases that obey the Pauli exclusion principle.

Ernest Orlando Lawrence American invented the cyclotron. Paul Adrien Maurice Dirac British helped found quantum electrodynamics; predicted the existence of antimatter by combining quantum mechanics with special relativity. Alfred Kastler French discovered and developed optical methods for studying the Hertzian resonances that are produced when atoms interact with radio waves or microwaves.

Eugene Wigner Hungarian-born American contributed to theoretical atomic and nuclear physics; introduced concept of the nuclear cross section. Cecil F. Powell British developed the photographic emulsion method of studying nuclear processes; discovered the charged pion. Ernest Walton Irish co-invented the first particle accelerator. Pavel A. Carl David Anderson American discovered the positron and the muon. Felix Bloch Swiss-born American contributed to development of the NMR technique; measured the magnetic moment of the neutron; contributed to the theory of metals. Sir Nevill F. Mott British contributed to theoretical condensed-matter physics by applying quantum theory to complex phenomena in solids; calculated cross section for relativistic Coulomb scattering.

Hans Bethe German-born American contributed to theoretical nuclear physics, especially concerning the mechanism for energy production in stars. Maria Goeppert-Mayer German-born American advanced shell model of nuclear structure. Ernst Ruska German designed the first electron microscope. Shin-Ichiro Tomonaga Japanese co-developed quantum electrodynamics. Hans D. Jensen German advanced shell model of nuclear structure.

Edwin M. McMillan American made discoveries concerning the transuranium elements. Hideki Yukawa Japanese predicted existence of the pion. John Bardeen American co-discovered the transistor effect; developed theory of superconductivity. Il'ja M. Lev Landau Soviet contributed to condensed matter theory on phenomena of superfluidity and superconductivity. Subramanyan Chandrasekhar Indian-born American made important theoretical contributions concerning the structure and evolution of stars, especially white dwarfs.

William Shockley American co-discovered the transistor effect. Luis Walter Alvarez American constructed huge bubble chambers and discovered many short-lived hadrons; advanced the impact theory for the extinction of the dinosaurs. William Fowler American studied nuclear reactions of astrophysical significance; developed, with others, a theory of the formation of chemical elements in the universe. Polykarp Kusch American experimentally established that the electron has an anomalous magnetic moment and made a precision determination of its magnitude.

Edward Mills Purcell American developed method of nuclear resonance absorption that permitted the absolute determination of nuclear magnetic moments; co-discovered a line in the galactic radiospectrum caused by atomic hydrogen. Glenn T. Seaborg American co-discovered plutonium and all further transuranium elements through element Willis E.

Lamb, Jr. Robert Hofstadter American measured charge distributions in atomic nuclei with high-energy electron scattering; measured the charge and magnetic-moment distributions in the proton and neutron.

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Norman F. Ramsey, Jr. Clifford G. Shull American developed a neutron scattering technique in which a neutron diffraction pattern is produced that may be used to determine the atomic structure of a material. Charles H. Townes American created first maser using ammonia to produce coherent microwave radiation. Bertram N. Brockhouse Canadian developed the technique of neutron spectroscopy for studies of condensed matter. Richard P. Feynman American co-developed quantum electrodynamics; created a new formalism for practical calculations by introducing a graphical method called Feynman diagrams.

Frederick Reines American established, together with Clyde L. Cowan, Jr. Julian Schwinger American co-developed quantum electrodynamics. Kai M. Siegbahn Swedish contributed to the development of high-resolution electron spectroscopy. Nicolaas Bloembergen Dutch-born American contributed to the development of laser spectroscopy. Owen Chamberlain American co-discovered the antiproton. Yoichiro Nambu Japanese-born American contributed to elementary particle theory; recognized the role played by spontaneous symmetry-breaking in analogy with superconductivity theory; formulated QCD quantum chromodynamics , the gauge theory of color.

Andrei Sakharov Russian father of the Soviet hydrogen bomb; awarded the Nobel Peace Prize for his struggle for human rights, for disarmament, and for cooperation between all nations. Heisenberg only proved relation 2 for the special case of Gaussian states. Throughout the main body of his original paper, written in German, Heisenberg used the word, "Ungenauigkeit" "indeterminacy" , [2] to describe the basic theoretical principle. Only in the endnote did he switch to the word, "Unsicherheit" "uncertainty".

When the English-language version of Heisenberg's textbook, The Physical Principles of the Quantum Theory , was published in , however, the translation "uncertainty" was used, and it became the more commonly used term in the English language thereafter.

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The principle is quite counter-intuitive, so the early students of quantum theory had to be reassured that naive measurements to violate it were bound always to be unworkable. One way in which Heisenberg originally illustrated the intrinsic impossibility of violating the uncertainty principle is by utilizing the observer effect of an imaginary microscope as a measuring device.

He imagines an experimenter trying to measure the position and momentum of an electron by shooting a photon at it. The combination of these trade-offs implies that no matter what photon wavelength and aperture size are used, the product of the uncertainty in measured position and measured momentum is greater than or equal to a lower limit, which is up to a small numerical factor equal to Planck's constant. The Copenhagen interpretation of quantum mechanics and Heisenberg's Uncertainty Principle were, in fact, seen as twin targets by detractors who believed in an underlying determinism and realism.

According to the Copenhagen interpretation of quantum mechanics, there is no fundamental reality that the quantum state describes, just a prescription for calculating experimental results. There is no way to say what the state of a system fundamentally is, only what the result of observations might be. Albert Einstein believed that randomness is a reflection of our ignorance of some fundamental property of reality, while Niels Bohr believed that the probability distributions are fundamental and irreducible, and depend on which measurements we choose to perform.

Einstein and Bohr debated the uncertainty principle for many years. Wolfgang Pauli called Einstein's fundamental objection to the uncertainty principle "the ideal of the detached observer" phrase translated from the German :. Observation cannot create an element of reality like a position, there must be something contained in the complete description of physical reality which corresponds to the possibility of observing a position, already before the observation has been actually made. It is precisely this kind of postulate which I call the ideal of the detached observer.

The first of Einstein's thought experiments challenging the uncertainty principle went as follows:. A similar analysis with particles diffracting through multiple slits is given by Richard Feynman. Bohr was present when Einstein proposed the thought experiment which has become known as Einstein's box. Einstein argued that "Heisenberg's uncertainty equation implied that the uncertainty in time was related to the uncertainty in energy, the product of the two being related to Planck's constant. The box could be weighed before a clockwork mechanism opened an ideal shutter at a chosen instant to allow one single photon to escape.

The change of mass tells the energy of the emitted light. In this manner, said Einstein, one could measure the energy emitted and the time it was released with any desired precision, in contradiction to the uncertainty principle. Bohr spent a sleepless night considering this argument, and eventually realized that it was flawed. He pointed out that if the box were to be weighed, say by a spring and a pointer on a scale, "since the box must move vertically with a change in its weight, there will be uncertainty in its vertical velocity and therefore an uncertainty in its height above the table.

Furthermore, the uncertainty about the elevation above the earth's surface will result in an uncertainty in the rate of the clock," [79] because of Einstein's own theory of gravity's effect on time. Bohr was compelled to modify his understanding of the uncertainty principle after another thought experiment by Einstein. Measuring one particle, Einstein realized, would alter the probability distribution of the other, yet here the other particle could not possibly be disturbed.

This example led Bohr to revise his understanding of the principle, concluding that the uncertainty was not caused by a direct interaction. But Einstein came to much more far-reaching conclusions from the same thought experiment. He believed the "natural basic assumption" that a complete description of reality would have to predict the results of experiments from "locally changing deterministic quantities" and therefore would have to include more information than the maximum possible allowed by the uncertainty principle.

In , John Bell showed that this assumption can be falsified, since it would imply a certain inequality between the probabilities of different experiments. Experimental results confirm the predictions of quantum mechanics, ruling out Einstein's basic assumption that led him to the suggestion of his hidden variables.

These hidden variables may be "hidden" because of an illusion that occurs during observations of objects that are too large or too small. This illusion can be likened to rotating fan blades that seem to pop in and out of existence at different locations and sometimes seem to be in the same place at the same time when observed. This same illusion manifests itself in the observation of subatomic particles.

Both the fan blades and the subatomic particles are moving so fast that the illusion is seen by the observer. Therefore, it is possible that there would be predictability of the subatomic particles behavior and characteristics to a recording device capable of very high speed tracking Ironically this fact is one of the best pieces of evidence supporting Karl Popper 's philosophy of invalidation of a theory by falsification-experiments. That is to say, here Einstein's "basic assumption" became falsified by experiments based on Bell's inequalities.

For the objections of Karl Popper to the Heisenberg inequality itself, see below. While it is possible to assume that quantum mechanical predictions are due to nonlocal, hidden variables, and in fact David Bohm invented such a formulation, this resolution is not satisfactory to the vast majority of physicists.

The question of whether a random outcome is predetermined by a nonlocal theory can be philosophical, and it can be potentially intractable. If the hidden variables are not constrained, they could just be a list of random digits that are used to produce the measurement outcomes. To make it sensible, the assumption of nonlocal hidden variables is sometimes augmented by a second assumption—that the size of the observable universe puts a limit on the computations that these variables can do.

A nonlocal theory of this sort predicts that a quantum computer would encounter fundamental obstacles when attempting to factor numbers of approximately 10, digits or more; a potentially achievable task in quantum mechanics. Karl Popper approached the problem of indeterminacy as a logician and metaphysical realist. This directly contrasts with the Copenhagen interpretation of quantum mechanics, which is non-deterministic but lacks local hidden variables. In , Popper published Zur Kritik der Ungenauigkeitsrelationen Critique of the Uncertainty Relations in Naturwissenschaften , [85] and in the same year Logik der Forschung translated and updated by the author as The Logic of Scientific Discovery in , outlining his arguments for the statistical interpretation.

In , he further developed his theory in Quantum theory and the schism in Physics , writing:.

But they have been habitually misinterpreted by those quantum theorists who said that these formulae can be interpreted as determining some upper limit to the precision of our measurements. Thus, uncertainty in the many-worlds interpretation follows from each observer within any universe having no knowledge of what goes on in the other universes. Some scientists including Arthur Compton [88] and Martin Heisenberg [89] have suggested that the uncertainty principle, or at least the general probabilistic nature of quantum mechanics, could be evidence for the two-stage model of free will.

One critique, however, is that apart from the basic role of quantum mechanics as a foundation for chemistry, nontrivial biological mechanisms requiring quantum mechanics are unlikely, due to the rapid decoherence time of quantum systems at room temperature. There is reason to believe that violating the uncertainty principle also strongly implies the violation of the second law of thermodynamics. From Wikipedia, the free encyclopedia. Foundational principle in quantum physics.

For other uses, see Uncertainty principle disambiguation. Classical mechanics Old quantum theory Bra—ket notation Hamiltonian Interference. Advanced topics. Quantum annealing Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum gravity Quantum information science Quantum machine learning Perturbation theory quantum mechanics Relativistic quantum mechanics Scattering theory Spontaneous parametric down-conversion Quantum statistical mechanics. Main article: Introduction to quantum mechanics. Propagation of de Broglie waves in 1d—real part of the complex amplitude is blue, imaginary part is green.

The probability shown as the colour opacity of finding the particle at a given point x is spread out like a waveform, there is no definite position of the particle. As the amplitude increases above zero the curvature reverses sign, so the amplitude begins to decrease again, and vice versa—the result is an alternating amplitude: a wave.

Main article: Wave packet. Main article: Matrix mechanics. Main articles: Quantum harmonic oscillator and Stationary state. Position blue and momentum red probability densities for an initial Gaussian distribution. Note the tradeoff between the widths of the distributions.

Main article: Coherent state. Main article: Particle in a box. Main article: Heisenberg's microscope. Main article: Bohr—Einstein debates. Main article: Popper's experiment. Main article: Many-worlds interpretation. Afshar experiment Canonical commutation relation Correspondence principle Correspondence rules Gromov's non-squeezing theorem Discrete Fourier transform Uncertainty principle Einstein's thought experiments Heisenbug Introduction to quantum mechanics Operationalization Observer effect information technology Observer effect physics Quantum indeterminacy Quantum non-equilibrium Quantum tunnelling Physics and Beyond book Stronger uncertainty relations Weak measurement.

Current Science. Physical Review Letters. Bibcode : PhRvL. Landau , E. Lifshitz Quantum Mechanics: Non-Relativistic Theory. Pergamon Press. Online copy. This fact is experimentally well-known for example in quantum optics see e. Matters, U. Beck, J. Cooper, M. Raymer; Cooper, J. A , 48 4 : —, Bibcode : PhRvA.. D , 23 8 : —, Bibcode : PhRvD.. American Journal of Physics. Bibcode : AmJPh..

Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron
Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron
Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron
Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron
Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron
Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron
Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron
Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron
Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron

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