Semi Classical Analysis
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Semiclassical Analysis
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Author : Maciej Zworski
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Semiclassical Analysis written by Maciej Zworski 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 2012 with Mathematics categories.
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
An Introduction To Semiclassical And Microlocal Analysis
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Author : André Bach
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-02
An Introduction To Semiclassical And Microlocal Analysis written by André Bach 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 2002-01-02 with Mathematics categories.
This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semi-classical theory.
Semi Classical Analysis
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Author : Victor Guillemin
language : en
Publisher:
Release Date : 2013
Semi Classical Analysis written by Victor Guillemin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Fourier integral operators categories.
Mathematical Concepts Of Quantum Mechanics
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Author : Stephen J. Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-24
Mathematical Concepts Of Quantum Mechanics written by Stephen J. Gustafson 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 2011-09-24 with Mathematics categories.
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.
Spectral Asymptotics In The Semi Classical Limit
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Author : Mouez Dimassi
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-16
Spectral Asymptotics In The Semi Classical Limit written by Mouez Dimassi 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 1999-09-16 with Mathematics categories.
Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.
Kam Theory And Semiclassical Approximations To Eigenfunctions
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Author : Vladimir F. Lazutkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Kam Theory And Semiclassical Approximations To Eigenfunctions written by Vladimir F. Lazutkin 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 Mathematics categories.
It is a surprising fact that so far almost no books have been published on KAM theory. The first part of this book seems to be the first monographic exposition of this subject, despite the fact that the discussion of KAM theory started as early as 1954 (Kolmogorov) and was developed later in 1962 by Arnold and Moser. Today, this mathematical field is very popular and well known among physicists and mathematicians. In the first part of this Ergebnisse-Bericht, Lazutkin succeeds in giving a complete and self-contained exposition of the subject, including a part on Hamiltonian dynamics. The main results concern the existence and persistence of KAM theory, their smooth dependence on the frequency, and the estimate of the measure of the set filled by KAM theory. The second part is devoted to the construction of the semiclassical asymptotics to the eigenfunctions of the generalized Schrödinger operator. The main result is the asymptotic formulae for eigenfunctions and eigenvalues, using Maslov`s operator, for the set of eigenvalues of positive density in the set of all eigenvalues. An addendum by Prof. A.I. Shnirelman treats eigenfunctions corresponding to the "chaotic component" of the phase space.
Symplectic Geometry And Quantum Mechanics
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Author : Maurice A. de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-06
Symplectic Geometry And Quantum Mechanics written by Maurice A. de Gosson 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 2006-08-06 with Mathematics categories.
This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.
Microlocal Analysis For Differential Operators
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Author : Alain Grigis
language : en
Publisher: Cambridge University Press
Release Date : 1994-03-03
Microlocal Analysis For Differential Operators written by Alain Grigis 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 1994-03-03 with Mathematics categories.
This book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
Semiclassical Analysis Witten Laplacians And Statistical Mechanics
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Author : Bernard Helffer
language : en
Publisher: World Scientific
Release Date : 2002-09-10
Semiclassical Analysis Witten Laplacians And Statistical Mechanics written by Bernard Helffer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-10 with Mathematics categories.
This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality.
Diffraction Effects In Semiclassical Scattering
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Author : H. M. Nussenzveig
language : en
Publisher: Cambridge University Press
Release Date : 1992-07-23
Diffraction Effects In Semiclassical Scattering written by H. M. Nussenzveig 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 1992-07-23 with Science categories.
This book deals with the theory of critical effects in semiclassical scattering, in which the standard approximations break down. Such critical effects are responsible for phenomena such as rainbows and glories.