Quantum Scattering Theory For Several Particle Systems

Author : L.D. Faddeev,S.P. Merkuriev
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 49,8 Mb
Release : 2013-04-18
Category : Science
ISBN : 9789401728324

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Quantum Scattering Theory for Several Particle Systems by L.D. Faddeev,S.P. Merkuriev Pdf

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,Christian Gerard
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 47,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662034033

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Scattering Theory of Classical and Quantum N-Particle Systems by Jan Derezinski,Christian Gerard Pdf

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,John Dirk Walecka
Publisher : Courier Corporation
Page : 640 pages
File Size : 55,9 Mb
Release : 2012-03-08
Category : Science
ISBN : 9780486134758

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Quantum Theory of Many-Particle Systems by Alexander L. Fetter,John Dirk Walecka Pdf

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 : Hiroshi Isozaki
Publisher : Springer Nature
Page : 411 pages
File Size : 47,8 Mb
Release : 2023-08-28
Category : Science
ISBN : 9789819937042

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Many-Body Schrödinger Equation by Hiroshi Isozaki Pdf

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 : John W. Negele
Publisher : CRC Press
Page : 474 pages
File Size : 44,5 Mb
Release : 2018-03-05
Category : Science
ISBN : 9780429966477

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Quantum Many-particle Systems by John W. Negele Pdf

This book explains the fundamental concepts and theoretical techniques used to understand the properties of quantum systems having large numbers of degrees of freedom. A number of complimentary approaches are developed, including perturbation theory; nonperturbative approximations based on functional integrals; general arguments based on order parameters, symmetry, and Fermi liquid theory; and stochastic methods.

Author : Christian Gérard
Publisher : Unknown
Page : 258 pages
File Size : 41,9 Mb
Release : 2014-05-22
Category : SCIENCE
ISBN : 1470413175

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Multiparticle Quantum Scattering in Constant Magnetic Fields by Christian Gérard Pdf

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

Author : Harry L. Morrison
Publisher : Unknown
Page : 372 pages
File Size : 54,7 Mb
Release : 1963
Category : Science
ISBN : UOM:39015017220743

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The Quantum Theory of Many-particle Systems by Harry L. Morrison Pdf

Author : Christian Gérard,Izabella Łaba
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 54,8 Mb
Release : 2002
Category : Few-body problem
ISBN : 9780821829196

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Multiparticle Quantum Scattering in Constant Magnetic Fields by Christian Gérard,Izabella Łaba Pdf

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.

Author : Léon Hove
Publisher : Unknown
Page : 272 pages
File Size : 55,5 Mb
Release : 1961
Category : Quantum theory
ISBN : UOM:39015078644336

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Problems in Quantum Theory of Many-particle Systems by Léon Hove Pdf

Author : Luiz Felipe Canto,M. S. Hussein
Publisher : World Scientific
Page : 646 pages
File Size : 49,6 Mb
Release : 2013
Category : Science
ISBN : 9789814329842

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Scattering Theory of Molecules, Atoms and Nuclei by Luiz Felipe Canto,M. S. Hussein Pdf

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.

Author : Kuzemsky Alexander Leonidovich
Publisher : World Scientific
Page : 1260 pages
File Size : 42,6 Mb
Release : 2017-02-24
Category : Science
ISBN : 9789813145658

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Statistical Mechanics And The Physics Of Many-particle Model Systems by Kuzemsky Alexander Leonidovich Pdf

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.

Author : Dmitri R. Yafaev
Publisher : Springer
Page : 185 pages
File Size : 49,7 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540451709

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Scattering Theory: Some Old and New Problems by Dmitri R. Yafaev Pdf

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.

Author : Dzevad Belkic
Publisher : CRC Press
Page : 388 pages
File Size : 49,9 Mb
Release : 2020-01-15
Category : Science
ISBN : 9781420033649

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Principles of Quantum Scattering Theory by Dzevad Belkic Pdf

Scattering is one of the most powerful methods used to study the structure of matter, and many of the most important breakthroughs in physics have been made by means of scattering. Nearly a century has passed since the first investigations in this field, and the work undertaken since then has resulted in a rich literature encompassing both experimental and theoretical results. In scattering, one customarily studies collisions among nuclear, sub-nuclear, atomic or molecular particles, and as these are intrinsically quantum systems, it is logical that quantum mechanics is used as the basis for modern scattering theory. In Principles of Quantum Scattering Theory, the author judiciously combines physical intuition and mathematical rigour to present various selected principles of quantum scattering theory. As always in physics, experiment should be used to ultimately validate physical and mathematical modelling, and the author presents a number of exemplary illustrations, comparing theoretical and experimental cross sections in a selection of major inelastic ion-atom collisions at high non-relativistic energies. Quantum scattering theory, one of the most beautiful theories in physics, is also very rich in mathematics. Principles of Quantum Scattering Theory is intended primarily for graduate physics students, but also for non-specialist physicists for whom the clarity of exposition should aid comprehension of these mathematical complexities.

Author : Roger G Newton
Publisher : Springer
Page : 745 pages
File Size : 45,6 Mb
Release : 2014-04-18
Category : Science
ISBN : 3642881300

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Scattering Theory of Waves and Particles by Roger G Newton Pdf

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.

Author : Eberhard K. U. Gross,GROSS,E. Runge,O. Heinonen
Publisher : CRC Press
Page : 448 pages
File Size : 54,6 Mb
Release : 1991-01-01
Category : Science
ISBN : 0750300728

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Many-Particle Theory, by Eberhard K. U. Gross,GROSS,E. Runge,O. Heinonen Pdf

The quantum theory of many-particle systems has applications in various branches of physics including condensed matter, atomic, molecular, nuclear and high-energy. An understanding of this theory is therefore important to most students of physics and Many-Particle Theory is an excellent introduction to the subject. Many-Particle Theory presents a detailed and logical account of the theory and techniques used. Basic subjects such as Green's functions and Feynman diagrams are discussed in detail, and many examples and applications are given, such as the Hartee-Fock approximation, superconductivity and the Kondo problem. Due to the detailed derivations and the fact that only a grasp of basic quantum mechanics is assumed, the book is an ideal textbook for graduate students and teachers of physics. The comprehensive bibliography contains many recent books and articles for further studies. Many-Particle Theory is a translation of the second German edition, which is an expanded version of the popular first edition. All three authors, E K U Gross, E Runge and O Heinonen, are well respected researchers in the field.