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Books on the topic 'Electrons Wave functions'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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1

Auerbach, Assa. Interacting electrons and quantum magnetism. New York: Springer-Verlag, 1994.

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2

Yserentant, Harry. Regularity and Approximability of Electronic Wave Functions. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12248-4.

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3

Regularity and approximability of electronic wave functions. Heidelberg: Springer, 2010.

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4

Volker, Schmidt. Electron spectrometry of atoms using synchrotron radiation. Cambridge: Cambridge University Press, 1997.

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5

He, Sailing. Time domain wave-splittings and inverse problems. Oxford: Oxford University Press, 1998.

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6

Rudolf, Rabenstein, ed. Digital sound synthesis by physical modeling using the functional transformation method. New York: Kluwer Academic/Plenum Publishers, 2003.

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7

Auerbach, Assa. Interacting Electrons and Quantum Magnetism. Springer, 2012.

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8

Levin, Frank S. The Hydrogen Atom and Its Colorful Photons. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198808275.003.0010.

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The energies, kets and wave functions obtained from the Schrödinger equation for the hydrogen atom are examined in Chapter 9. Three quantum numbers are identified. The energies turn out to be the same as in the Bohr model, and an energy-level diagram appropriate to the quantum description is constructed. Graphs of the probability distributions are interpreted as the electron being in a “cloud” around the proton, rather than at a fixed position: the atom is fuzzy, not sharp-edged. The wavelengths of the five photons of the Balmer series are shown to be in the visible range. These photons are emitted when electrons transition from higher-excited states to the second lowest one, which means that electronic-type transitions underlie the presence of colors in our visible environment. The non-collapse of the atom, required by classical physics, is shown to arise from the structure of Schrödinger’s equation.
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9

Solymar, L., D. Walsh, and R. R. A. Syms. The electron. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0003.

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Discusses with some rigour the properties of electrons, based on the Schrodinger equation. Introduces the concepts of wave function, quantum-mechanical operators, and wave packets. Examples cover the electron meeting an infinitely long potential barrier and the passage of electrons through a finite barrier (which leads to the phenomenon of tunnelling).The electron in a potential well is also discussed, solving the problem both for a finite and for an infinite well, and finding the permissible energy levels. The chapter is concluded with the philosophical implications that arise from the quantum-mechanical approach. Two limericks relevant to the subject are quoted.
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10

Solymar, L., D. Walsh, and R. R. A. Syms. The band theory of solids. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0007.

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The solution of Schrodinger’s equation is discussed for a model in which atoms are represented by potential wells, from which the band structure follows. Three further models are discussed, the Ziman model (which is based on the effect of Bragg reflection upon the wave functions), and the Feynman model (based on coupled equations), and the tight binding model (based on a more realistic solution of the Schrödinger equation). The concept of effective mass is introduced, followed by the effective number of electrons. The difference between metals and insulators based on their band structure is discussed. The concept of holes is introduced. The band structure of divalent metals is explained. For finite temperatures the Fermi–Dirac function is combined with band theory whence the distinction between insulators and semiconductors is derived.
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11

Yserentant, Harry. Regularity and Approximability of Electronic Wave Functions. Springer, 2010.

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12

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.
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13

Levin, Frank S. Quantum Boxes, Stringed Instruments. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198808275.003.0008.

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Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.
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14

Morawetz, Klaus. Deep Impurities with Collision Delay. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0017.

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The linearised nonlocal kinetic equation is solved analytically for impurity scattering. The resulting response function provides the conductivity, plasma oscillation and Fermi momentum. It is found that virial corrections nearly compensate the wave-function renormalizations rendering the conductivity and plasma mode unchanged. Due to the appearance of the correlated density, the Luttinger theorem does not hold and the screening length is influenced. Explicit results are given for a typical semiconductor. Elastic scattering of electrons by impurities is the simplest but still very interesting dissipative mechanism in semiconductors. Its simplicity follows from the absence of the impurity dynamics, so that individual collisions are described by the motion of an electron in a fixed potential.
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15

Beenakker, Carlo W. J. Classical and quantum optics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.36.

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This article focuses on applications of random matrix theory (RMT) to both classical optics and quantum optics, with emphasis on optical systems such as disordered wave guides and chaotic resonators. The discussion centres on topics that do not have an immediate analogue in electronics, either because they cannot readily be measured in the solid state or because they involve aspects (such as absorption, amplification, or bosonic statistics) that do not apply to electrons. The article first considers applications of RMT to classical optics, including optical speckle and coherent backscattering, reflection from an absorbing random medium, long-range wave function correlations in an open resonator, and direct detection of open transmission channels. It then discusses applications to quantum optics, namely: the statistics of grey-body radiation, lasing in a chaotic cavity, and the effect of absorption on the reflection eigenvalue statistics in a multimode wave guide.
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16

Hansen, Thorkild, and Arthur D. Yaghjian. Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications (IEEE Press Series on Electromagnetic Wave Theory). Wiley-IEEE Press, 1999.

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17

AUGMENTED SPHERICAL WAVE METHOD LECTURE. SPRINGER, 2013.

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18

Solymar, L., D. Walsh, and R. R. A. Syms. The hydrogen atom and the periodic table. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0004.

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Investigates the energy levels in a configuration when a heavy positive particle (proton) and a light negative particle (electron) are present. The wave functions and permissible energy levels are derived from Schrödinger's equation. The role of quantum numbers is discussed. Electron spin and Pauli’s exclusion principle are introduced. The properties of the elements in the periodic table are discussed, based on the properties of the hydrogen atom. Exceptions when such a simple approach does not work are further discussed.
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19

L, Malli G., North Atlantic Treaty Organization. Scientific Affairs Division., and NATO Advanced Study Institute on Relativistic and Electron Correlation Effects in Molecules and Solids (1992 : Vancouver, B.C.), eds. Relativistic and electron correlation effects in molecules and solids. New York: Plenum Press, 1994.

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20

The Augmented Spherical Wave Method: A Comprehensive Treatment (Lecture Notes in Physics). Springer, 2007.

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21

R, Taylor Peter, and Ames Research Center, eds. General contraction of Gaussian basis sets: II. Atomic natural orbitals and the calculation of atomic and molecular properties. [Moffett Field, Calif: NASA Ames Research Center, 1989.

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22

Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Pr, 1985.

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23

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1990.

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24

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1990.

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25

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1986.

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26

Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1991.

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27

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1985.

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28

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1987.

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29

Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1993.

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30

(Editor), Benjamin Kazan, ed. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1993.

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31

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1988.

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32

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1991.

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33

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1989.

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34

(Editor), Benjamin Kazan, ed. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1991.

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35

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1990.

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36

Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1989.

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37

Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1989.

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38

Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1988.

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39

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1986.

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40

Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1993.

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41

Hawkes, Peter W. Advances in Electronics and Electron Physics (Advances in Imaging and Electron Physics). Academic Press, 1986.

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42

Lutsenko, V. I., I. V. Lutsenko, D. O. Popov, and I. V. Popov. Remote sensing of the environment using the radiation of existing ground and space radio systems. PH “Akademperiodyka”, 2020. http://dx.doi.org/10.15407/akademperiodyka.429.345.

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Possibilities of using existing ground (TV centers, broadcasting stations) and space (global navigation satellite systems) radio systems for solving the problem of remote sensing and monitoring of the environment and objects in it are considered. The methods of diagnostics of the troposphere, description of the refractive index with the use of semi-Markov processes and atomic functions of Kravchenko-Rvacheva are proposed. The seasonal and altitudinal dependencies of radio-meteorological parameters and radio-climatic features of Ukraine were studied. Technologies for determining the effective gradient of the refractive index by damping factor of the VHF signals of television centers on the OTH routes in the zone of the near geometric shadow, on the angles of radioa "rise" and "sets" of the AES, detection of precipitation zones by the fluctuations of the pseudoranges and changes of the coordinates estimates, parameters of the surface of the earth by the fluctuations of the GNSS signals. Reviewers: Head of the Department of Radio waves propagation in the natural environments of the O. Ya. Usikov Institute for Radiophysics and Electronics NASU, Doctor of Physical and Mathematical Sciences, Professor Kivva F.V., Professor of the Department of Designing Radioelectronic Devices of Aircraft of the National Aerospace University. M.E. Zhukovsky (KhAI), Doctor of Technical Sciences, Professor Volosyuk V.K.
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43

Trautmann, Lutz, and Rudolf Rabenstein. Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method. Springer, 2003.

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44

Trautmann, Lutz. Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method. Springer, 2012.

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