Quantum Scattering Theory For Several Particle Systems
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Quantum Scattering Theory For Several Particle Systems
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Author : L.D. Faddeev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
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 2013-04-18 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 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.
Quantum Theory Of Many Particle Systems
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Author : Alexander L. Fetter
language : en
Publisher: Courier Corporation
Release Date : 2012-03-08
Quantum Theory Of Many Particle Systems written by Alexander L. Fetter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-08 with Science categories.
Self-contained treatment of nonrelativistic many-particle systems discusses both formalism and applications in terms of ground-state (zero-temperature) formalism, finite-temperature formalism, canonical transformations, and applications to physical systems. 1971 edition.
Many Body Schr Dinger Equation
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Author : Hiroshi Isozaki
language : en
Publisher: Springer Nature
Release Date : 2023-08-28
Many Body Schr Dinger Equation written by Hiroshi Isozaki and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Science categories.
Spectral properties for Schrödinger operators are a major concern in quantum mechanics both in physics and in mathematics. For the few-particle systems, we now have sufficient knowledge for two-body systems, although much less is known about N-body systems. The asymptotic completeness of time-dependent wave operators was proved in the 1980s and was a landmark in the study of the N-body problem. However, many problems are left open for the stationary N-particle equation. Due to the recent rapid development of computer power, it is now possible to compute the three-body scattering problem numerically, in which the stationary formulation of scattering is used. This means that the stationary theory for N-body Schrödinger operators remains an important problem of quantum mechanics. It is stressed here that for the three-body problem, we have a satisfactory stationary theory. This book is devoted to the mathematical aspects of the N-body problem from both the time-dependent and stationary viewpoints. The main themes are:(1) The Mourre theory for the resolvent of self-adjoint operators(2) Two-body Schrödinger operators—Time-dependent approach and stationary approach(3) Time-dependent approach to N-body Schrödinger operators(4) Eigenfunction expansion theory for three-body Schrödinger operatorsCompared with existing books for the many-body problem, the salient feature of this book consists in the stationary scattering theory (4). The eigenfunction expansion theorem is the physical basis of Schrödinger operators. Recently, it proved to be the basis of inverse problems of quantum scattering. This book provides necessary background information to understand the physical and mathematical basis of Schrödinger operators and standard knowledge for future development.
Multiparticle Quantum Scattering In Constant Magnetic Fields
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Author : Christian Gérard
language : en
Publisher:
Release Date : 2014-05-22
Multiparticle Quantum Scattering In Constant Magnetic Fields written by Christian Gérard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-22 with SCIENCE categories.
This monograph offers a rigorous mathematical treatment of the scattering theory of quantum N-particle systems in an external constant magnetic field. In particular, it addresses the question of asymptotic completeness, a classification of all possible trajectories of such systems according to their asymptotic behaviour. The book adopts the so-called time-dependent approach to scattering theory, which relies on a direct study of the Schrodinger unitary group for large times. The modern methods of spectral and scattering theory introduced in the 1980's and 1990's, including the Mourre theory of positive commutators, propagation estimates, and geometrical techniques, are presented and heavily used. Additionally, new methods were developed by the authors in order to deal with the (much less understood) phenomena due to the presence of the magnetic field. The book is a good starting point for graduate students and researchers in mathematical physics who wish to move into this area of research. It includes expository material, research work previously available only in the form of journal articles, as well as some new unpublished results. The treatment of the subject is comprehensive an
The Quantum Theory Of Many Particle Systems
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Author : Harry L. Morrison
language : en
Publisher:
Release Date : 1963
The Quantum Theory Of Many Particle Systems written by Harry L. Morrison and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Science categories.
Problems In Quantum Theory Of Many Particle Systems
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Author : Léon Hove
language : en
Publisher:
Release Date : 1961
Problems In Quantum Theory Of Many Particle Systems written by Léon Hove and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Quantum theory categories.
Statistical Mechanics And The Physics Of Many Particle Model Systems
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Author : Kuzemsky Alexander Leonidovich
language : en
Publisher: World Scientific
Release Date : 2017-02-24
Statistical Mechanics And The Physics Of Many Particle Model Systems written by Kuzemsky Alexander Leonidovich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-24 with Science categories.
The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models. This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography. The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.
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 atomic/molecular scattering from those of nuclear systems, are shown to be the same once physical units such as energy and 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 also lean heavily on semi-classical methods to explain the physics of quantum scattering OCo especially the interference seen in the angle dependence of the cross section. Having in mind a wide 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.
Multiparticle Quantum Scattering In Constant Magnetic Fields
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Author : Christian Gérard
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Multiparticle Quantum Scattering In Constant Magnetic Fields written by Christian Gérard 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 2002 with Few-body problem categories.
This monograph offers a rigorous mathematical treatment of the scattering theory of quantum N-particle systems in an external constant magnetic field. In particular, it addresses the question of asymptotic completeness, a classification of all possible trajectories of such systems according to their asymptotic behaviour. The book adopts the so-called time-dependent approach to scattering theory, which relies on a direct study of the Schrodinger unitary group for large times. The modern methods of spectral and scattering theory introduced in the 1980's and 1990's, including the Mourre theory of positive commutators, propagation estimates, and geometrical techniques, are presented and heavily used. Additionally, new methods were developed by the authors in order to deal with the (much less understood) phenomena due to the presence of the magnetic field. The book is a good starting point for graduate students and researchers in mathematical physics who wish to move into this area of research. It includes expository material, research work previously available only in the form of journal articles, as well as some new unpublished results. The treatment of the subject is comprehensive and largely self-contained, and the text is carefully written with attention to detail.