Scattering Theory
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Scattering Theory Of Waves And Particles
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Author : R.G. Newton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Scattering Theory Of Waves And Particles written by R.G. Newton 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 2013-11-27 with Science categories.
Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to incorporate all areas of new develop ment. Since among the newer books on scattering theory there are three excellent volumes that treat the subject from a much more abstract mathe matical point of view (Lax and Phillips on electromagnetic scattering, Amrein, Jauch and Sinha, and Reed and Simon on quantum scattering), I have refrained from adding material concerning the abundant new mathe matical results on time-dependent formulations of scattering theory. The only exception is Dollard's beautiful "scattering into cones" method that connects the physically intuitive and mathematically clean wave-packet description to experimentally accessible scattering rates in a much more satisfactory manner than the older procedure. Areas that have been substantially augmented are the analysis of the three-dimensional Schrodinger equation for non central potentials (in Chapter 10), the general approach to multiparticle reaction theory (in Chapter 16), the specific treatment of three-particle scattering (in Chapter 17), and inverse scattering (in Chapter 20). The additions to Chapter 16 include an introduction to the two-Hilbert space approach, as well as a derivation of general scattering-rate formulas. Chapter 17 now contains a survey of various approaches to the solution of three-particle problems, as well as a discussion of the Efimov effect.
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 : 1997-06-05
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 1997-06-05 with Mathematics 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.
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.
Scattering Theory Revised Edition
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Author : Peter D. Lax
language : en
Publisher: Academic Press
Release Date : 1990-02-22
Scattering Theory Revised Edition written by Peter D. Lax and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-02-22 with Mathematics categories.
This revised edition of a classic book, which established scattering theory as an important and fruitful area of research, reflects the wealth of new results discovered in the intervening years. This new, revised edition should continue to inspire researchers to expand the application of the original ideas proposed by the authors.
Scattering Theory
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Author : John R. Taylor
language : en
Publisher: Courier Corporation
Release Date : 2006-05-26
Scattering Theory written by John R. Taylor and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-26 with Technology & Engineering categories.
This graduate-level text is intended for any student of physics who requires a thorough grounding in the quantum theory of nonrelativistic scattering. It is designed for readers who are already familiar with the general principles of quantum mechanics and who have some small acquaintance with scattering theory. Study of this text will allow students of atomic or nuclear physics to begin reading the literature and tackling real problems, with a complete grasp of the underlying principles. For students of high-energy physics, it provides the necessary background for later study of relativistic problems. Topics are presented in terms of the simplest relevant example, so that scattering theory can be learned by becoming familiar with all of the basic concepts — the S operator, cross sections, the T matrix, and so forth — in their simplest context. The time-dependent approach to the subject is emphasized, starting with the use of time-dependent formalism to define all of the basic concepts and the subsequent introduction of the time-independent theory as a tool for computation and for establishing certain general properties. Problems at the end of each chapter improve and supplement readers' grasp of the material.
Scattering Theory
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Author : Harald Friedrich
language : en
Publisher: Springer
Release Date : 2015-11-20
Scattering Theory written by Harald Friedrich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-20 with Science categories.
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
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.
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.
Scattering Theory Of Molecules Atoms And Nuclei
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Author : Luiz Felipe Canto
language : en
Publisher: World Scientific
Release Date : 2013
Scattering Theory Of Molecules Atoms And Nuclei written by Luiz Felipe Canto 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 with Science categories.
The aim of the book is to give a coherent and comprehensive account of quantum scattering theory with applications to atomic, molecular and nuclear systems. The motivation for this is to supply the necessary theoretical tools to calculate scattering observables of these many-body systems. Concepts, which are seemingly different for the atomic/molecular scattering from those for nuclear systems, are shown to be the same once the physical units such as energy, length are diligently clarified. Many-body resonances excited in nuclear systems are the same as those in atomic systems and come under the name of Feshbach resonances. We clarify this. We also lean heavily on semi-classical methods to explain the physics of quantum scattering and especially the interference seen in the angle dependence of the cross section. Having in mind a wider readership, the book includes sections on scattering in two dimensions, which is of use in surface physics. Several problems are also included at the end of each of the chapters.
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