Solvable Models In Quantum Mechanics

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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 : 49,8 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 : 53,9 Mb
Release : 2024-06-30
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.

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 : 49,8 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
Solvable Models in Quantum Mechanics Book PDF

Author : Sergio Albeverio
Publisher : Unknown
Page : 488 pages
File Size : 53,7 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.

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 : 55,7 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.

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 : 48,5 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

Classical Systems in Quantum Mechanics

Pavel Bóna
Classical Systems in Quantum Mechanics Book PDF

Author : Pavel Bóna
Publisher : Springer Nature
Page : 243 pages
File Size : 40,8 Mb
Release : 2020-06-23
Category : Science
ISBN : 9783030450700

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Classical Systems in Quantum Mechanics by Pavel Bóna Pdf

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".

Solvable One-Dimensional Multi-State Models for Statistical and Quantum Mechanics

Rajendran Saravanan,Aniruddha Chakraborty
Solvable One Dimensional Multi State Models for Statistical and Quantum Mechanics Book PDF

Author : Rajendran Saravanan,Aniruddha Chakraborty
Publisher : Springer Nature
Page : 186 pages
File Size : 40,8 Mb
Release : 2021-11-14
Category : Science
ISBN : 9789811666544

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Solvable One-Dimensional Multi-State Models for Statistical and Quantum Mechanics by Rajendran Saravanan,Aniruddha Chakraborty Pdf

This book highlights the need for studying multi-state models analytically for understanding the physics of molecular processes. An intuitive picture about recently solved models of statistical and quantum mechanics is drawn along with presenting the methods developed to solve them. The models are relevant in the context of molecular processes taking place in gaseous phases and condensed phases, emphasized in the introduction. Chapter 1 derives the arisal of multi-state models for molecular processes from the full Hamiltonian description. The model equations are introduced and the literature review presented in short. In Chapter 2, the time-domain methods to solve Smoluchowski-based reaction-diffusion systems with single-state and two-state descriptions are discussed. Their corresponding analytical results derive new equilibrium concepts in reversible reactions and studies the effect of system and molecular parameters in condensed-phase chemical dynamics. In Chapter 3, time-domain methods to solve quantum scattering problems are developed. Along side introducing a brand new solvable model in quantum scattering, it discusses transient features of quantum two-state models. In interest with electronic transitions, a new solvable two-state model with localized non-adiabatic coupling is also presented. The book concludes by proposing the future scope of the model, thereby inviting new research in this fundamentally important and rich applicable field.​

A Mathematical Primer on Quantum Mechanics

Alessandro Teta
A Mathematical Primer on Quantum Mechanics Book PDF

Author : Alessandro Teta
Publisher : Springer
Page : 265 pages
File Size : 51,5 Mb
Release : 2018-04-17
Category : Science
ISBN : 9783319778938

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A Mathematical Primer on Quantum Mechanics by Alessandro Teta Pdf

This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

Exactly Solved Models in Statistical Mechanics

Rodney J. Baxter
Exactly Solved Models in Statistical Mechanics Book PDF

Author : Rodney J. Baxter
Publisher : Elsevier
Page : 498 pages
File Size : 45,5 Mb
Release : 2016-06-12
Category : Science
ISBN : 9781483265940

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Exactly Solved Models in Statistical Mechanics by Rodney J. Baxter Pdf

Exactly Solved Models in Statistical Mechanics

Thermodynamics of One-Dimensional Solvable Models

Minoru Takahashi
Thermodynamics of One Dimensional Solvable Models Book PDF

Author : Minoru Takahashi
Publisher : Cambridge University Press
Page : 268 pages
File Size : 40,6 Mb
Release : 2005-09-15
Category : Science
ISBN : 0521019796

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Thermodynamics of One-Dimensional Solvable Models by Minoru Takahashi Pdf

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.

Exploring Quantum Mechanics

Victor Galitski,Boris Karnakov,Vladimir Kogan
Exploring Quantum Mechanics Book PDF

Author : Victor Galitski,Boris Karnakov,Vladimir Kogan
Publisher : OUP Oxford
Page : 904 pages
File Size : 54,7 Mb
Release : 2013-02-28
Category : Science
ISBN : 9780191634048

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Exploring Quantum Mechanics by Victor Galitski,Boris Karnakov,Vladimir Kogan Pdf

A series of seminal technological revolutions has led to a new generation of electronic devices miniaturized to such tiny scales where the strange laws of quantum physics come into play. There is no doubt that, unlike scientists and engineers of the past, technology leaders of the future will have to rely on quantum mechanics in their everyday work. This makes teaching and learning the subject of paramount importance for further progress. Mastering quantum physics is a very non-trivial task and its deep understanding can only be achieved through working out real-life problems and examples. It is notoriously difficult to come up with new quantum-mechanical problems that would be solvable with a pencil and paper, and within a finite amount of time. This book remarkably presents some 700+ original problems in quantum mechanics together with detailed solutions covering nearly 1000 pages on all aspects of quantum science. The material is largely new to the English-speaking audience. The problems have been collected over about 60 years, first by the lead author, the late Prof. Victor Galitski, Sr. Over the years, new problems were added and the material polished by Prof. Boris Karnakov. Finally, Prof. Victor Galitski, Jr., has extended the material with new problems particularly relevant to modern science.

Solvable One-Dimensional Multi-State Models for Statistical and Quantum Mechanics

Rajendran Saravanan,Aniruddha Chakraborty
Solvable One Dimensional Multi State Models for Statistical and Quantum Mechanics Book PDF

Author : Rajendran Saravanan,Aniruddha Chakraborty
Publisher : Unknown
Page : 0 pages
File Size : 42,5 Mb
Release : 2021
Category : Electronic
ISBN : 9811666555

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Solvable One-Dimensional Multi-State Models for Statistical and Quantum Mechanics by Rajendran Saravanan,Aniruddha Chakraborty Pdf

This book highlights the need for studying multi-state models analytically for understanding the physics of molecular processes. An intuitive picture about recently solved models of statistical and quantum mechanics is drawn along with presenting the methods developed to solve them. The models are relevant in the context of molecular processes taking place in gaseous phases and condensed phases, emphasized in the introduction. Chapter 1 derives the arisal of multi-state models for molecular processes from the full Hamiltonian description. The model equations are introduced and the literature review presented in short. In Chapter 2, the time-domain methods to solve Smoluchowski-based reaction-diffusion systems with single-state and two-state descriptions are discussed. Their corresponding analytical results derive new equilibrium concepts in reversible reactions and studies the effect of system and molecular parameters in condensed-phase chemical dynamics. In Chapter 3, time-domain methods to solve quantum scattering problems are developed. Along side introducing a brand new solvable model in quantum scattering, it discusses transient features of quantum two-state models. In interest with electronic transitions, a new solvable two-state model with localized non-adiabatic coupling is also presented. The book concludes by proposing the future scope of the model, thereby inviting new research in this fundamentally important and rich applicable field.

Elements of Classical and Quantum Integrable Systems

Gleb Arutyunov
Elements of Classical and Quantum Integrable Systems Book PDF

Author : Gleb Arutyunov
Publisher : Springer
Page : 414 pages
File Size : 50,9 Mb
Release : 2019-07-23
Category : Science
ISBN : 9783030241988

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Elements of Classical and Quantum Integrable Systems by Gleb Arutyunov Pdf

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

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 : 55,9 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: