Quasi Exactly Solvable Models In Quantum Mechanics
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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.
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.
Quantum Theory Of Tunneling 2nd Edition
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Author : Mohsen Razavy
language : en
Publisher: World Scientific
Release Date : 2013-12-17
Quantum Theory Of Tunneling 2nd Edition written by Mohsen Razavy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Science categories.
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.
Quantum Theory Of Tunneling
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Author : Mohsen Razavy
language : en
Publisher: World Scientific
Release Date : 2003-01-29
Quantum Theory Of Tunneling written by Mohsen Razavy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-29 with Science categories.
This book provides a comprehensive introduction to the theoretical foundations of quantum tunneling, stressing the basic physics underlying the applications. The topics addressed include exponential and nonexponential decay processes and the application of scattering theory to tunneling problems. In addition to the Schrödinger equation approach, the path integral, Heisenberg's equations and the phase space method are all used to study the motion of a particle under the barrier. Extensions to the multidimensional cases and tunneling of particles with internal degrees of freedom are also considered. Furthermore, recent advances concerning time delay and tunneling times and some of the problems associated with their measurement are also discussed. Finally, some examples of tunneling in atomic, molecular, nuclear and condensed matter physics are presented.
Low Dimensional Nanoscale Systems On Discrete Spaces
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Author : Erhardt Papp
language : en
Publisher: World Scientific
Release Date : 2007-04-24
Low Dimensional Nanoscale Systems On Discrete Spaces written by Erhardt Papp and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-24 with Technology & Engineering categories.
The area of low-dimensional quantum systems on discrete spaces is a rapidly growing research field lying at the interface between quantum theoretical developments, like discrete and q-difference equations, and tight binding superlattice models in solid-state physics. Systems on discrete spaces are promising candidates for applications in several areas. Indeed, the dynamic localization of electrons on the 1D lattice under the influence of an external electric field serves to describe time-dependent transport in quantum wires, linear optical absorption spectra, and the generation of higher harmonics. Odd-even parity effects and the flux dependent oscillations of total persistent currents in discretized rings can also be invoked. Technological developments are then provided by conductance calculations characterizing 1D conductors, junctions between rings and leads or rings and dots, and by quantum LC-circuits. Accordingly, the issues presented in this book are important starting points for the design of novel nanodevices.
Symmetry In Physics
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Author : Robert T. Sharp
language : en
Publisher: American Mathematical Soc.
Release Date : 2004-01-01
Symmetry In Physics written by Robert T. Sharp 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 2004-01-01 with Science categories.
Papers in this volume are based on the Workshop on Symmetries in Physics held at the Centre de recherches mathematiques (University of Montreal) in memory of Robert T. Sharp. Contributed articles are on a variety of topics revolving around the theme of symmetry in physics. The preface presents a biographical and scientific retrospect of the life and work of Robert Sharp. Other articles in the volume represent his diverse range of interests, including representation theoretic methods for Lie algebras, quantization techniques and foundational considerations, modular group invariants and applications to conformal models, various physical models and equations, geometric calculations with symmetries, and pedagogical methods for developing spatio-temporal intuition. The book is suitable for graduate students and researchers interested in group theoretic methods, symmetries, and mathematical physics.
Group Theoretical Methods In Physics
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Author : G.S Pogosyan
language : en
Publisher: CRC Press
Release Date : 2005-05-01
Group Theoretical Methods In Physics written by G.S Pogosyan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-01 with Mathematics categories.
This book discusses group theoretical methods and their applications in physics, chemistry, and biology. It covers traditional subjects including Lie group and representation theory, special functions, foundations of quantum mechanics, and elementary particle, nuclear, atomic, and molecular physics. More recent areas discussed are supersymmetry, superstrings and quantum gravity, integrability, nonlinear systems and quantum chaos, semigroups, time asymmetry and resonances, condensed matter, and statistical physics. Topics such as linear and nonlinear optics, quantum computing, discrete systems, and signal analysis have only in the last few years become part of the group theorists' turf.
Quantum Mechanics I
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Author : S. Rajasekar
language : en
Publisher: CRC Press
Release Date : 2022-11-28
Quantum Mechanics I written by S. Rajasekar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-28 with Science categories.
Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems. This fully updated new edition addresses many topics not typically found in books at this level, including: Bound state solutions of quantum pendulum Morse oscillator Solutions of classical counterpart of quantum mechanical systems A criterion for bound state Scattering from a locally periodic potential and reflection-less potential Modified Heisenberg relation Wave packet revival and its dynamics An asymptotic method for slowly varying potentials Klein paradox, Einstein-Podolsky-Rosen (EPR) paradox, and Bell’s theorem Delayed-choice experiments Fractional quantum mechanics Numerical methods for quantum systems A collection of problems at the end of each chapter develops students’ understanding of both basic concepts and the application of theory to various physically important systems. This book, along with the authors’ follow-up Quantum Mechanics II: Advanced Topics, provides students with a broad, up-to-date introduction to quantum mechanics. Print Versions of this book also include access to the ebook version.
An Introduction To Inverse Problems In Physics
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Author : Mohsen Razavy
language : en
Publisher: World Scientific
Release Date : 2020-05-21
An Introduction To Inverse Problems In Physics written by Mohsen Razavy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-21 with Science categories.
This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist dealing with these aspects of the inverse problems.The emphasis here is on finding numerical solutions to complicated equations. A detailed discussion is presented on the use of continued fractional expansion, its power and its limitation as applied to various physical problems. In particular, the inverse problem for discrete form of the wave equation is given a detailed exposition and applied to atomic and nuclear scattering, in the latter for elastic as well as inelastic collision. This technique is also used for inverse problem of geomagnetic induction and one-dimensional electrical conductivity. Among other topics covered are the inverse problem of torsional vibration, and also a chapter on the determination of the motion of a body with reflecting surface from its reflection coefficient.
Quantum Field Theory And String Theory
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Author : L. Baulieu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Field Theory And String Theory written by L. Baulieu 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.
The Cargese Workshop "Quantum Field Theory and String Theory" was held from May 10 to May 21, 1993. The broad spectrum of the work presented at the Workshop was the reflec tion of a time of intensive search for new ways of solving some of the most fun damental problems in string theory, quantum gravity and non-perturbative field theory. A number of talks indicated the emergence of new promising domains of investigation. It is this very diversity of topics which, in our opinion, represents one of the most attractive features of the present volume which we hope will provide a good orientation in the abundant flow of ideas and publications in modern quantum field theory. Many contributions to the present proceedings are concerned with two di mensional quantum field theory. The continuous advances in the domain of two dimensional integrable theories on the lattice as well as in the continuum, including conformal field theories, Liouville field theory and matrix models of two dimensional quantum gravity are very well represented. Other papers address physically realistic (and therefore very complicated) problems like de veloped turbulence, the Hofstadter problem, higher dimensional gravity and phenomenological strings. A new elegant class of topological field theories is presented. New ideas in the string representation of multicolor quantum chromo dynamics were widely discussed at the Workshop, more particularly the example of the exactly solvable two dimensional case.