Quasi Exactly Solvable Models In Quantum Mechanics

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Quasi-Exactly Solvable Models in Quantum Mechanics

A.G Ushveridze
Quasi Exactly Solvable Models in Quantum Mechanics Book PDF

Author : A.G Ushveridze
Publisher : Routledge
Page : 268 pages
File Size : 41,5 Mb
Release : 2017-07-12
Category : Science
ISBN : 9781351420310

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Quasi-Exactly Solvable Models in Quantum Mechanics by A.G Ushveridze Pdf

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

Sergio Albeverio,Friedrich Gesztesy,Raphael Hoegh-Krohn,Helge Holden
Solvable Models in Quantum Mechanics Book PDF

Author : Sergio Albeverio,Friedrich Gesztesy,Raphael Hoegh-Krohn,Helge Holden
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642882012

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Solvable Models in Quantum Mechanics by Sergio Albeverio,Friedrich Gesztesy,Raphael Hoegh-Krohn,Helge Holden Pdf

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.

Solvable Models in Quantum Mechanics

S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, H. Holden, and an appendix by P. Exner
Solvable Models in Quantum Mechanics Book PDF

Author : S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, H. Holden, and an appendix by P. Exner
Publisher : American Mathematical Soc.
Page : 508 pages
File Size : 47,6 Mb
Release : 2024-07-01
Category : Quantum theory
ISBN : 082186940X

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Solvable Models in Quantum Mechanics by S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, H. Holden, and an appendix by P. Exner Pdf

"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.

Quantum Many-Body Systems in One Dimension

Zachary N C Ha
Quantum Many Body Systems in One Dimension Book PDF

Author : Zachary N C Ha
Publisher : World Scientific
Page : 168 pages
File Size : 48,6 Mb
Release : 1996-09-13
Category : Science
ISBN : 9789814500371

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Quantum Many-Body Systems in One Dimension by Zachary N C Ha Pdf

The main theme of the book is the intimate connection between the two families of exactly solvable models: the inverse-square exchange (ISE) and the nearest-neighbor exchange (NNE) models. The latter are better known as the Bethe-Ansatz solvable models and include the Heisenberg spin chain, t–J models and Hubbard models. The former, the Calogero–Sutherland family of models, are simple to solve and contain essentially the same physics as the NNE family. The author introduces and discusses current topics, such as the Luttinger liquid concept, fractional statistics, and spin–charge separation, in the context of the explicit models. Contents:IntroductionHeisenberg Spin ChainThe 1D Hubbard ModelModels with Inverse-Square ExchangeStrings in Long-Range Interaction ModelElementary Excitations of t-J ModelFractional Statistics in One-Dimension: View from an Exactly Solvable ModelConcluding Remarks Readership: Graduate students, researchers in statistical mechanics, mathematical physics and condensed matter physics. keywords:Quantum;Many-Body;One;Inverse Square;Exchange;Luttinger;Fractional Statistics

Exactly Solvable Models in Many-Body Theory

N H March,G G N Angilella
Exactly Solvable Models in Many Body Theory Book PDF

Author : N H March,G G N Angilella
Publisher : World Scientific
Page : 348 pages
File Size : 40,9 Mb
Release : 2016-05-27
Category : Science
ISBN : 9789813140165

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Exactly Solvable Models in Many-Body Theory by N H March,G G N Angilella Pdf

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. Contents:Low-Order Density MatricesSolvable Models for Small Clusters of FermionsSmall Clusters of BosonsAnyon Statistics with ModelsSuperconductivity and SuperfluidityExact Results for an Isolated Impurity in a SolidPair Potential and Many-Body Force Models for LiquidsAnderson Localization in Disordered SystemsStatistical Field Theory: Especially Models of Critical ExponentsRelativistic FieldsTowards Quantum GravityAppendices Readership: Graduate students and researchers in condensed matter theory.

Solvable Models in Quantum Mechanics

Sergio Albeverio
Solvable Models in Quantum Mechanics Book PDF

Author : Sergio Albeverio
Publisher : Unknown
Page : 488 pages
File Size : 42,9 Mb
Release : 2004
Category : Quantum theory
ISBN : 1470430266

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Solvable Models in Quantum Mechanics by Sergio Albeverio Pdf

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.

Quantum Hamilton-Jacobi Formalism

A. K. Kapoor,Prasanta K. Panigrahi,S. Sree Ranjani
Quantum Hamilton Jacobi Formalism Book PDF

Author : A. K. Kapoor,Prasanta K. Panigrahi,S. Sree Ranjani
Publisher : Springer Nature
Page : 122 pages
File Size : 51,7 Mb
Release : 2022-10-05
Category : Science
ISBN : 9783031106248

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Quantum Hamilton-Jacobi Formalism by A. K. Kapoor,Prasanta K. Panigrahi,S. Sree Ranjani Pdf

This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allowscomputation of eigenvalues of quantum mechanical potential problems without solving for thewave function. The examples presented include exotic potentials such as quasi-exactly solvablemodels and Lame an dassociated Lame potentials. A careful application of boundary conditionsoffers an insight into the nature of solutions of several potential models. Advancedundergraduates having knowledge of complex variables and quantum mechanics will find thisas an interesting method to obtain the eigenvalues and eigen-functions. The discussion oncomplex zeros of the wave function gives intriguing new results which are relevant foradvanced students and young researchers. Moreover, a few open problems in research arediscussed as well, which pose a challenge to the mathematically oriented readers.

Perspectives on Solvable Models

Uwe Grimm,Michael Baake
Perspectives on Solvable Models Book PDF

Author : Uwe Grimm,Michael Baake
Publisher : World Scientific
Page : 308 pages
File Size : 44,8 Mb
Release : 1995-01-23
Category : Science
ISBN : 9789814501040

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Perspectives on Solvable Models by Uwe Grimm,Michael Baake Pdf

This volume consists of a collection of recent research articles dedicated to Vladimir Rittenberg on the occasion of his 60th birthday. Various aspects of solvable models in different areas of theoretical and mathematical physics are covered. Particular topics include diffusion, self-organized criticality, classical and quantum spin chains, two-dimensional lattice models, quantum algebras, and conformal field theory. The list of contributing authors contains altogether 34 names, including among others, Baxter, Cardy, Itzykson, Martin, McCoy, Nahm, Pearce and de Vega. Contents:PrefaceExact Steady States of Asymmetric Diffusion and Two-Species Annihilation with Back Reaction from the Ground State of Quantum Spin Models (F C Alcaraz)Schrödinger Invariance in Discrete Stochastic Systems (M Henkel & G Schütz)Exact Thermostatic Results for the n-Vector Model on the Harmonic Chain (G Junker & H Leschke)Non-Hermitian Tricriticality in the Blume-Capel Model with Imaginary Field (G von Gehlen)Fusion of A–D–E Lattice Models (Y-K Zhou & P A Pearce)A Critical Ising Model on the Labyrinth (M Baake et al.)Quantum Superspin Chains (T H Baker & P D Jarvis)q-Deformations of Quantum Spin Chains with Exact Valence-Bond Ground States (M T Batchelor & C M Yung)The Tensor Product of Tensor Operators Over Quantum Algebras: Some Applications to Quantum Spin Chains (M Scheunert)Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras (A J Bracken et al.)Sigma Models with (2,2) World Sheet Supersymmetry (F Delduc & E Sokatchev)and other papers Readership: Theoretical physicists. keywords:

Panorama of Contemporary Quantum Mechanics

Trong Tuong Truong
Panorama of Contemporary Quantum Mechanics Book PDF

Author : Trong Tuong Truong
Publisher : BoD – Books on Demand
Page : 110 pages
File Size : 49,7 Mb
Release : 2019-12-04
Category : Science
ISBN : 9781839626654

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Panorama of Contemporary Quantum Mechanics by Trong Tuong Truong Pdf

This book is devoted to recent developments in quantum mechanics. After an Introductory chapter, Chapter 2 describes the cooperative spontaneous lasing mechanism in gas in three level systems and their possible quantum retardation effects. Chapter 3 is concerned with the evolution of states of large quantum particle systems via marginal correlation operators. Chapter 4 studies the effects of electronic transfer using ab initio quantum calculation methods to access biological macromolecular system behaviors. Chapter 5 concentrates on new features of supersymmetric quantum mechanics using the adjunction of boson-fermion symmetry. The book will be of interest to graduate and Ph.D students as well as scientists from various backgrounds who are concerned with quantum effects.

Submissive Quantum Mechanics

Boris Nikolaevich Zakharʹev,Vladimir Emelʹi︠a︡novich Chabanov
Submissive Quantum Mechanics Book PDF

Author : Boris Nikolaevich Zakharʹev,Vladimir Emelʹi︠a︡novich Chabanov
Publisher : Unknown
Page : 280 pages
File Size : 40,5 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015073949821

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Submissive Quantum Mechanics by Boris Nikolaevich Zakharʹev,Vladimir Emelʹi︠a︡novich Chabanov Pdf

Use of this unique book will permit correction of the present defect in quantum education throughout the world. The new breakthrough in quantum mechanics was recently achieved due to the inverse problem approach. It allows finding infinite (!) number of exactly solvable models instead of only about ten previously known. It means an incomparable more convenient basis for the quantum education and countless instructive examples of the precise control of the spectral parameters. That was impossible to imagine in the previous quantum theory. Another great achievement was the discovery of qualitative rules of transformations of the most elementary wave constituents, their separate bumps. This opened the 'black box' of the above mentioned exact models and intensifies many times their usefulness. One acquires the notion about the simplest "bricks" and building blocks of potential and wave transformations. It means a real quantum ABC to acquire the quantum literacy and facilitate the future discoveries. So, one gains the absolutely unexpected ability of immediate prediction how, in principle, to achieve the given properties of the constructed objects. An unprecedented combination of qualitative simplicity and clarity with absolute exactness was achieved. Unlike the numerous books on quantum mechanics, mainly compilations, this one has no analogues. Being first hand information it is utmost intelligible due to computer visualisations. It is not a substitution of the traditional books, but a fundamental, strengthening and simplifying addition to them enlarging and deepening the understanding of the subject instead of previously unintuitive and approximate approach.

From Classical to Quantum Mechanics

Giampiero Esposito,Giuseppe Marmo,George Sudarshan
From Classical to Quantum Mechanics Book PDF

Author : Giampiero Esposito,Giuseppe Marmo,George Sudarshan
Publisher : Cambridge University Press
Page : 612 pages
File Size : 54,6 Mb
Release : 2004-03-11
Category : Science
ISBN : 9781139450546

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From Classical to Quantum Mechanics by Giampiero Esposito,Giuseppe Marmo,George Sudarshan Pdf

This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.

Lie Theory and Its Applications in Physics

H-D Doebner,J Hilgert,V K Dobrev
Lie Theory and Its Applications in Physics Book PDF

Author : H-D Doebner,J Hilgert,V K Dobrev
Publisher : World Scientific
Page : 284 pages
File Size : 51,6 Mb
Release : 1996-10-16
Category : Electronic
ISBN : 9789814547086

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Lie Theory and Its Applications in Physics by H-D Doebner,J Hilgert,V K Dobrev Pdf

There is an apparent trend towards geometrization of physical theories. During the last 20 years, the most successful mathematical models for the description and understanding of physical systems have been based on the Lie theory in its widest sense and various generalizations, for example, deformations of it. This proceedings volume reflects part of the development. On the mathematical side, they report on representations of Lie algebras, quantization procedures, non-commutative geometry, quantum groups, etc. Furthermore, possible physical applications of these techniques are discussed (e.g. quantization of classical systems, derivations of evolution equations, discrete and deformed physical systems). This volume complements the book Generalized Symmetries in Physics, published by World Scientific in 1994. Contents:Representation Theory and Quantization MethodsNoncommutative Geometry, Quantum Algebras and Applications to Relativistic and Nonrelativistic SystemsSpecial Applications to Physical Systems and Their Generalized ModelsRepresentation Theory and Quantization Methods Readership: Mathematicians and physicists. keywords:

Lie Algebras, Cohomology, and New Applications to Quantum Mechanics,

Niky Kamran,Peter J. Olver
Lie Algebras Cohomology and New Applications to Quantum Mechanics Book PDF

Author : Niky Kamran,Peter J. Olver
Publisher : American Mathematical Soc.
Page : 310 pages
File Size : 50,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851692

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Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, by Niky Kamran,Peter J. Olver Pdf

This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrodinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.

Quantum Theory of Tunneling

Mohsen Razavy
Quantum Theory of Tunneling Book PDF

Author : Mohsen Razavy
Publisher : World Scientific
Page : 792 pages
File Size : 52,5 Mb
Release : 2013-12-17
Category : Science
ISBN : 9789814525039

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Quantum Theory of Tunneling by Mohsen Razavy Pdf

In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined. In addition, by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and nuclear physics are presented and solved. Contents:A Brief History of Quantum TunnelingSome Basic Questions Concerning Quantum TunnelingSimple Solvable ProblemsTime-Dependence of the Wave Function in One-Dimensional TunnelingSemiclassical ApproximationsGeneralization of the Bohr–Sommerfeld Quantization Rule and Its Application to Quantum TunnelingGamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying StateTunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable BarriersClassical Descriptions of Quantum TunnelingTunneling in Time-Dependent BarriersDecay Width and the Scattering TheoryThe Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling ProblemsPath Integral and Its Semi-Classical Approximation in Quantum TunnelingHeisenberg's Equations of Motion for TunnelingWigner Distribution Function in Quantum TunnelingDecay Widths of Siegert States, Complex Scaling and Dilatation TransformationMultidimensional Quantum TunnelingGroup and Signal VelocitiesTime-Delay, Reflection Time Operator and Minimum Tunneling TimeMore About Tunneling TimeTunneling of a System with Internal Degrees of FreedomMotion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped ObjectRelativistic Formulation of Quantum TunnelingInverse Problems of Quantum TunnelingSome Examples of Quantum Tunneling in Atomic and Molecular PhysicsSome Examples in Condensed Matter PhysicsAlpha Decay Readership: Graduate students and researchers in theoretical, mathematical, condensed matter and nuclear physics, as well as theoretical chemistry. Keywords:Quantum Tunneling;Quantum Clocks;Electromagnetic Wave Propagation;Semiclassical Approximations

Exploring Quantum Mechanics

Viktor Mikhaĭlovich Galit︠s︡kiĭ,Boris Karnakov,Victor Galitski,Vladimir Kogan,Vladimir Ilʹich Kogan
Exploring Quantum Mechanics Book PDF

Author : Viktor Mikhaĭlovich Galit︠s︡kiĭ,Boris Karnakov,Victor Galitski,Vladimir Kogan,Vladimir Ilʹich Kogan
Publisher : Oxford University Press
Page : 898 pages
File Size : 42,5 Mb
Release : 2013-02-28
Category : Science
ISBN : 9780199232710

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Exploring Quantum Mechanics by Viktor Mikhaĭlovich Galit︠s︡kiĭ,Boris Karnakov,Victor Galitski,Vladimir Kogan,Vladimir Ilʹich Kogan Pdf

A unique resource on quantum physics that contains original problems with solutions that can be used by teachers and students of quantum mechanics at graduate and undergraduate level. Numerous tricks-of-the-trade in solving quantum physics problems are included which can also be used by professional researchers in all fields of modern physics.