Mathematical Scattering Theory
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Mathematical Scattering Theory
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Author : Dmitri_ Rauel_evich I_Afaev
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-03-10
Mathematical Scattering Theory written by Dmitri_ Rauel_evich I_Afaev 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 2010-03-10 with Mathematics categories.
The main subject of this book is applications of methods of scattering theory to differential operators, primarily the Schrodinger operator. There are two different trends in scattering theory for differential operators. The first one relies on the abstract scattering theory. The second one is almost independent of it. In this approach the abstract theory is replaced by a concrete investigation of the corresponding differential equation. In this book both of these trends are presented. The first half of this book begins with the summary of the main results of the general scattering theory of the previous book by the author, Mathematical Scattering Theory: General Theory, American Mathematical Society, 1992. The next three chapters illustrate basic theorems of abstract scattering theory, presenting, in particular, their applications to scattering theory of perturbations of differential operators with constant coefficients and to the analysis of the trace class method. In the second half of the book direct methods of scattering theory for differential operators are presented. After considering the one-dimensional case, the author returns to the multi-dimensional problem and discusses various analytical methods and tools appropriate for the analysis of differential operators, including, among others, high- and low-energy asymptotics of the Green function, the scattering matrix, ray and eikonal expansions. The book is based on graduate courses taught by the author at Saint-Petersburg (Russia) and Rennes (France) Universities and is oriented towards a reader interested in studying deep aspects of scattering theory (for example, a graduate student in mathematical physics).
Mathematical Scattering Theory
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Author : D. R. Yafaev
language : en
Publisher: American Mathematical Soc.
Release Date : 1992-09-09
Mathematical Scattering Theory written by D. R. Yafaev 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 1992-09-09 with Mathematics categories.
Preliminary facts Basic concepts of scattering theory Further properties of the WO Scattering for relatively smooth perturbations The general setup in stationary scattering theory Scattering for perturbations of trace class type Properties of the scattering matrix (SM) The spectral shift function (SSF) and the trace formula
Mathematical Scattering Theory
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Author : Baumgärtel
language : en
Publisher: Birkhäuser
Release Date : 2013-12-11
Mathematical Scattering Theory written by Baumgärtel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Science categories.
The aim of this book is to give a systematic and self-contained presentation of the Mathematical Scattering Theory within the framework of operator theory in Hilbert space. The term Mathematical Scattering Theory denotes that theory which is on the one hand the common mathematical foundation of several physical scattering theories (scattering of quantum objects, of classical waves and particles) and on the other hand a branch of operator theory devoted to the study of the behavior of the continuous part of perturbed operators (some authors also use the term Abstract Scattering Theory). EBBential contributions to the development of this theory are due to K. FRIEDRICHS, J. CooK, T. KATo, J. M. JAuCH, S. T. KURODA, M.S. BmMAN, M.G. KREiN, L. D. FAD DEEV, R. LAVINE, W. 0. AMREIN, B. SIMoN, D. PEARSON, V. ENss, and others. It seems to the authors that the theory has now reached a sufficiently developed state that a self-contained presentation of the topic is justified.
Scattering Theory Of Classical And Quantum N Particle Systems
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Author : Jan Derezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Scattering Theory Of Classical And Quantum N Particle Systems written by Jan Derezinski 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 2013-03-09 with Science categories.
This monograph addresses researchers and students. It is a modern presentation of time-dependent methods for studying problems of scattering theory in the classical and quantum mechanics of N-particle systems. Particular attention is paid to long-range potentials. For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding. As a special feature of the book, the beautiful analogy between classical and quantum scattering theory (e.g., for N-body Hamiltonians) is presented with deep insight into the physical and mathematical problems.
Mathematical Scattering Theory
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Author : H. Baumgärtel
language : de
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1983-12-31
Mathematical Scattering Theory written by H. Baumgärtel and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-31 with Science categories.
Keine ausführliche Beschreibung für "Mathematical Scattering Theory" verfügbar.
Iii Scattering Theory
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Author : Michael Reed
language : en
Publisher: Academic Press
Release Date : 1979-04-28
Iii Scattering Theory written by Michael Reed and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-04-28 with Mathematics categories.
Volume 3.
Mathematical Scattering Theory
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Author : Hellmut Baumgärtel
language : en
Publisher:
Release Date : 1988
Mathematical Scattering Theory written by Hellmut Baumgärtel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Scattering Theory Some Old And New Problems
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Author : Dmitri R. Yafaev
language : en
Publisher: Springer
Release Date : 2007-05-06
Scattering Theory Some Old And New Problems written by Dmitri R. Yafaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.
Quantum Scattering Theory For Several Particle Systems
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Author : L.D. Faddeev
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-08-31
Quantum Scattering Theory For Several Particle Systems written by L.D. Faddeev 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 1993-08-31 with Science categories.
The last decade witnessed an increasing interest of mathematicians in prob lems originated in mathematical physics. As a result of this effort, the scope of traditional mathematical physics changed considerably. New problems es pecially those connected with quantum physics make use of new ideas and methods. Together with classical and functional analysis, methods from dif ferential geometry and Lie algebras, the theory of group representation, and even topology and algebraic geometry became efficient tools of mathematical physics. On the other hand, the problems tackled in mathematical physics helped to formulate new, purely mathematical, theorems. This important development must obviously influence the contemporary mathematical literature, especially the review articles and monographs. A considerable number of books and articles appeared, reflecting to some extend this trend. In our view, however, an adequate language and appropriate methodology has not been developed yet. Nowadays, the current literature includes either mathematical monographs occasionally using physical terms, or books on theoretical physics focused on the mathematical apparatus. We hold the opinion that the traditional mathematical language of lem mas and theorems is not appropriate for the contemporary writing on mathe matical physics. In such literature, in contrast to the standard approaches of theoretical physics, the mathematical ideology must be utmost emphasized and the reference to physical ideas must be supported by appropriate mathe matical statements. Of special importance are the results and methods that have been developed in this way for the first time.
Mathematical Scattering Theory
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Author : D. R. Yafaev
language : en
Publisher:
Release Date : 1992
Mathematical Scattering Theory written by D. R. Yafaev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.