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Solvable Models In Quantum Mechanics

Solvable Models in Quantum Mechanics PDF
Author: S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, H. Holden, and an appendix by P. Exner
Publisher: American Mathematical Soc.
ISBN: 9780821869406
Size: 23.23 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages :
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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, Solvable Models In Quantum Mechanics Books available in PDF, EPUB, Mobi Format. Download Solvable Models In Quantum Mechanics books, 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 Schrodinger 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. The material is suitable for graduate students and researchers interested in quantum mechanics and Schrodinger operators.




Quasi Exactly Solvable Models In Quantum Mechanics

Quasi Exactly Solvable Models in Quantum Mechanics PDF
Author: A.G Ushveridze
Publisher: Routledge
ISBN: 1351420313
Size: 54.11 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 480
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Quasi Exactly Solvable Models In Quantum Mechanics

by A.G Ushveridze, Quasi Exactly Solvable Models In Quantum Mechanics Books available in PDF, EPUB, Mobi Format. Download Quasi Exactly Solvable Models In Quantum Mechanics books, 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

Solvable Models in Quantum Mechanics PDF
Author: Sergio Albeverio
Publisher: Springer Science & Business Media
ISBN: 3642882013
Size: 35.13 MB
Format: PDF
Category : Science
Languages : en
Pages : 452
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Solvable Models In Quantum Mechanics

by Sergio Albeverio, Solvable Models In Quantum Mechanics Books available in PDF, EPUB, Mobi Format. Download Solvable Models In Quantum Mechanics books, 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.




Exactly Solvable Models In Many Body Theory

Exactly Solvable Models in Many Body Theory PDF
Author: N H March
Publisher: World Scientific
ISBN: 981314016X
Size: 56.72 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 348
View: 1943

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Exactly Solvable Models In Many Body Theory

by N H March, Exactly Solvable Models In Many Body Theory Books available in PDF, EPUB, Mobi Format. Download Exactly Solvable Models In Many Body Theory books, 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.




Diffusion Quantum Theory And Radically Elementary Mathematics Mn 47

Diffusion  Quantum Theory  and Radically Elementary Mathematics   MN 47  PDF
Author: William G. Faris
Publisher: Princeton University Press
ISBN: 0691125457
Size: 48.16 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 256
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Diffusion Quantum Theory And Radically Elementary Mathematics Mn 47

by William G. Faris, Diffusion Quantum Theory And Radically Elementary Mathematics Mn 47 Books available in PDF, EPUB, Mobi Format. Download Diffusion Quantum Theory And Radically Elementary Mathematics Mn 47 books, Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.




Statistical Field Theory

Statistical Field Theory PDF
Author: Giuseppe Mussardo
Publisher: Oxford University Press
ISBN: 0199547580
Size: 15.54 MB
Format: PDF, ePub
Category : Science
Languages : en
Pages : 755
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Statistical Field Theory

by Giuseppe Mussardo, Statistical Field Theory Books available in PDF, EPUB, Mobi Format. Download Statistical Field Theory books, A thorough and pedagogical introduction to phase transitions and exactly solved models in statistical physics and quantum field theory.




Integrable Systems In Quantum Field Theory And Statistical Mechanics

Integrable Systems in Quantum Field Theory and Statistical Mechanics PDF
Author: M. Jimbo
Publisher: Elsevier
ISBN: 1483295257
Size: 29.75 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 682
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Integrable Systems In Quantum Field Theory And Statistical Mechanics

by M. Jimbo, Integrable Systems In Quantum Field Theory And Statistical Mechanics Books available in PDF, EPUB, Mobi Format. Download Integrable Systems In Quantum Field Theory And Statistical Mechanics books, Integrable Sys Quantum Field Theory