Quantum Scattering Theory for Several Particle Systems PDF Download
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Author: L.D. Faddeev
Publisher: Springer Science & Business Media
ISBN: 9401728321
Category : Science
Languages : en
Pages : 415
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Book Description
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.
Author: L.D. Faddeev
Publisher: Springer Science & Business Media
ISBN: 9401728321
Category : Science
Languages : en
Pages : 415
Get Book Here
Book Description
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.
Author: Jan Derezinski
Publisher: Springer Science & Business Media
ISBN: 3662034034
Category : Science
Languages : en
Pages : 448
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Book Description
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.
Author: Alexander L. Fetter
Publisher: Courier Corporation
ISBN: 048613475X
Category : Science
Languages : en
Pages : 626
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Book Description
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.
Author: Ta-you Wu
Publisher: Courier Corporation
ISBN: 0486320693
Category : Science
Languages : en
Pages : 530
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Book Description
This volume addresses the broad formal aspects and applications of the quantum theory of scattering in atomic and nuclear collisions. An encyclopedic source of pioneering work, it serves as a text for students and a reference for professionals in the fields of chemistry, physics, and astrophysics. The self-contained treatment begins with the general theory of scattering of a particle by a central field. Subsequent chapters explore particle scattering by a non-central field, collisions between composite particles, the time-dependent theory of scattering, and nuclear reactions. An examination of dispersion relations concludes the text. Numerous graphs, tables, and footnotes illuminate each chapter, in addition to helpful appendixes and bibliographies.
Author: A. G. Sitenko
Publisher: Elsevier
ISBN: 1483186822
Category : Science
Languages : en
Pages : 280
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Book Description
Lectures in Scattering Theory discusses problems in quantum mechanics and the principles of the non-relativistic theory of potential scattering. This book describes in detail the properties of the scattering matrix and its connection with physically observable quantities. This text presents a stationary formulation of the scattering problem and the wave functions of a particle found in an external field. This book also examines the analytic properties of the scattering matrix, dispersion relations, complex angular moments, as well as the separable representation of the scattering amplitude. The text also explains the method of factorizing the potential and the two-particle scattering amplitude, based on the Hilbert-Schmidt theorem for symmetric integral equations. In investigating the problem of scattering in a three-particle system, this book notes that the inapplicability of the Lippman-Schwinger equations can be fixed by appropriately re-arranging the equations. Faddeev equations are the new equations formed after such re-arrangements. This book also cites, as an example, the scattering of a spin-1/2 particle by a spinless particle (such as the scattering of a nucleon by a spinless nucleus). This text is suitable for students and professors dealing with quantum mechanics, theoretical nuclear physics, or other fields of advanced physics.
Author: W.D. Kraeft
Publisher: Springer Science & Business Media
ISBN: 146132159X
Category : Science
Languages : en
Pages : 306
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Book Description
The year 1985 represents a special anniversary for people dealing with Ooulomb systems. 200 years ago, in 1785, Oharles Auguste de Ooulomb (1736-1806) found "Ooulomb's law" for the interaction force between charged particles. The authors want to dedicate this book to the honour of the great pioneer of electrophysics. Recent statistical mechanics is mainly restricted to systems of neutral particles. Except for a few monographs and survey articles (see, e. g., IOHIMARU, 1973, 1982; KUDRIN, 1974; KLIMONTOVIOH, 1975; EBELING, KRAEFT and KREMP, 1976, 1979; KALMAN and CARINI, 1978; BAUS and HANSEN, 1980; GILL, 1981, VELO and WIGHT MAN, 1981; MATSUBARA, 1982) the extended material on charged particle systems, which is now available thanks to the efforts of many workers in statistical mechanics, is widely dispersed in many original articles. It is the aim of this monograph to represent at least some part of the known results on charged particle systems from a unified point of view. Here the method of Green's functions turns out to be a powerful method especially to overcome the difficulties connected with the statistical physics of charged particle systems; some of them are . mentioned in the introduction. Here we can point, e.g., to the appearance of bound states in a medium and their role as new entities.
Author: Hiroshi Isozaki
Publisher: Springer Nature
ISBN: 9819937043
Category : Science
Languages : en
Pages : 411
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Book Description
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.
Author: D.J. Thouless
Publisher: Courier Corporation
ISBN: 0486493571
Category : Science
Languages : en
Pages : 258
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Book Description
"Unabridged republication of the second edition of the work, originally published in the Pure and applied physics series by Academic Press, Inc., New York, in 1972"--Title page verso.
Author: Peter Bongaarts
Publisher: Springer
ISBN: 3319095617
Category : Science
Languages : en
Pages : 460
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Book Description
This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.
Author: Henrik Bruus
Publisher: Oxford University Press
ISBN: 0198566336
Category : Science
Languages : en
Pages : 458
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Book Description
The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.
