Solvable Models In Quantum Mechanics
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Solvable Models In Quantum Mechanics
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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Solvable Models In Quantum Mechanics written by Sergio Albeverio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.
Quasi Exactly Solvable Models In Quantum Mechanics
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Author : A.G Ushveridze
language : en
Publisher: Routledge
Release Date : 2017-07-12
Quasi Exactly Solvable Models In Quantum Mechanics written by A.G Ushveridze and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Science categories.
Exactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward. Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES Schrödinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics. Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.
Exactly Solvable Models In Many Body Theory
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Author : Norman H March
language : en
Publisher: World Scientific
Release Date : 2016-05-27
Exactly Solvable Models In Many Body Theory written by Norman H March and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-27 with Science categories.
The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.
Solvable Models In Quantum Mechanics
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Author : S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, H. Holden, and an appendix by P. Exner
language : en
Publisher: American Mathematical Soc.
Release Date :
Solvable Models In Quantum Mechanics written by S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, H. Holden, and an appendix by P. Exner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
"This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided. The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988."--Résumé de l'éditeur.
Quasi Exactly Solvable Models In Quantum Mechanics
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Author : A.G Ushveridze
language : en
Publisher: CRC Press
Release Date : 2017-07-12
Quasi Exactly Solvable Models In Quantum Mechanics written by A.G Ushveridze and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Science categories.
Exactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward. Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES Schrödinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics. Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.
Solvable Models In Quantum Mechanics
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Author : Sergio Albeverio
language : en
Publisher:
Release Date : 2004
Solvable Models In Quantum Mechanics written by Sergio Albeverio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Quantum theory categories.
This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations-where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution-are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different method.
Exactly Solved Models In Statistical Mechanics
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Author : Rodney J. Baxter
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Exactly Solved Models In Statistical Mechanics written by Rodney J. Baxter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Science categories.
Exploration of two-dimensional lattice models examines basic statistical mechanics, Ising models, spherical models, ice-type models, corner transfer matrices, and elliptic functions. 1982 edition, with author's 2007 update on subsequent developments.
Classical Systems In Quantum Mechanics
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Author : Pavel Bóna
language : en
Publisher: Springer Nature
Release Date : 2020-06-23
Classical Systems In Quantum Mechanics written by Pavel Bóna and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-23 with Science categories.
This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".
Thermodynamics Of One Dimensional Solvable Models
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Author : Minoru Takahashi
language : en
Publisher: Cambridge University Press
Release Date : 2005-09-15
Thermodynamics Of One Dimensional Solvable Models written by Minoru Takahashi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-15 with Science categories.
Exactly solvable models are very important in physics from a theoretical point of view and also from the experimentalist's perspective, because in such cases theoretical results and experimental results can be compared without ambiguity. This is a book about an important class of exactly solvable models in physics. The subject area is the Bethe-ansatz approach for a number of one-dimensional models, and the setting up of equations within this approach to determine the thermodynamics of these systems. It is a topic that crosses the boundaries among condensed matter physics, mathematics and field theory. The derivation and application of thermodynamic Bethe-ansatz equations for one-dimensional models are explained in detail. This technique is indispensable for physicists studying the low-temperature properties of one-dimensional substances. Written by the originator of much of the work in the subject, this book will be of great interest to theoretical condensed matter physicists.