An Introduction To Semiclassical And Microlocal Analysis
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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.
An Introduction To Semiclassical And Microlocal Analysis
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Author : Lina Martins
language : en
Publisher:
Release Date : 2014-01-15
An Introduction To Semiclassical And Microlocal Analysis written by Lina Martins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
An Introduction To Semiclassical And Microlocal Analysis
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Author : André Bach
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
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 2013-03-14 with Mathematics categories.
The following lecture notes correspond to a course taught for several years, first at the University of Paris-Nord (France) and then at the University of Bologna (Italy). They are mainly addressed to nonspecialists in the subject, and their purpose is to present in a pedagogical way most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard Coo pseudodifferential calculus and the analytic microlocal analysis are developed, in a context that remains intentionally global so that only the relevant difficulties of the theory are encountered. The main original ity lies in the fact that we derive all the main features of analytic microlocal analysis from a single a priori estimate, which turns out to be elementary once the Coo pseudodifferential calculus is established. Various detailed exercises are given at the end of the main chapters, most of them being easily solvable by students. Besides illustrating the main results of the lecture, their aim is also to introduce the reader to various further developments of the theory, such as the functional calculus of pseudodifferential operators, properties of the analytic wave front set, Gevrey classes, the use of coherent states, the notion of semiclassical measures, WKB constructions. Applications to the study of the Schrodinger operator are also discussed in the text, so that they may help the understanding of new notions or general results where they appear by replacing them in the context of quantum mechanics.
Microlocal Analysis And Precise Spectral Asymptotics
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Author : Victor Ivrii
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-05-20
Microlocal Analysis And Precise Spectral Asymptotics written by Victor Ivrii 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 1998-05-20 with Mathematics categories.
This long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates. The very powerful machinery of local and microlocal semiclassical spectral asymptotics is developed as well as methods in combining these asymptotics with spectral estimates. The rescaling technique should be mentioned as an easy as to use and very powerful tool. Many theorems, considered before as independent and difficult, now are just special cases of easy corollaries of the theorems proved in the book. Most of the results and almost all the proofs are as yet unpublished
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.
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.
Singularities Of Integrals
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Author : Frédéric Pham
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-22
Singularities Of Integrals written by Frédéric Pham 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 2011-04-22 with Mathematics categories.
Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
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.
An Introduction To Ordinary Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
An Introduction To Ordinary Differential Equations written by Ravi P. Agarwal 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 2008-12-10 with Mathematics categories.
Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.
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.