Scattering Theory Of Classical And Quantum N Particle Systems

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Scattering Theory of Classical and Quantum N-Particle Systems

Jan Derezinski,Christian Gerard
Scattering Theory of Classical and Quantum N Particle Systems Book PDF

Author : Jan Derezinski,Christian Gerard
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 51,5 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.

Quantum Scattering Theory for Several Particle Systems

L.D. Faddeev,S.P. Merkuriev
Quantum Scattering Theory for Several Particle Systems Book PDF

Author : L.D. Faddeev,S.P. Merkuriev
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 46,6 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.

Scattering Theory of Waves and Particles

Roger G. Newton
Scattering Theory of Waves and Particles Book PDF

Author : Roger G. Newton
Publisher : Courier Corporation
Page : 772 pages
File Size : 46,6 Mb
Release : 2002-01-01
Category : Science
ISBN : 9780486425351

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Scattering Theory of Waves and Particles by Roger G. Newton Pdf

This volume crosses the boundaries of physics' traditional subdivisions to treat scattering theory within the context of classical electromagnetic radiation, classical particle mechanics, and quantum mechanics. Includes updates on developments in three-particle collisions, scattering by noncentral potentials, and inverse scattering problems. 1982 edition.

Scattering Theory of Molecules, Atoms and Nuclei

Luiz Felipe Canto,M. S. Hussein
Scattering Theory of Molecules Atoms and Nuclei Book PDF

Author : Luiz Felipe Canto,M. S. Hussein
Publisher : World Scientific
Page : 646 pages
File Size : 46,8 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.

Scattering Theory in Mathematical Physics

J.A. Lavita,J.P. Marchand
Scattering Theory in Mathematical Physics Book PDF

Author : J.A. Lavita,J.P. Marchand
Publisher : Springer Science & Business Media
Page : 398 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401021470

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Scattering Theory in Mathematical Physics by J.A. Lavita,J.P. Marchand Pdf

These proceedings contain lectures given at the N.A.T.O. Advanced Study Institute entitled "Scattering Theory in Mathematics and Physics" held in Denver, Colorado, June 11-29, 1973. We have assembled the main series of lectures and some presented by other participants that seemed naturally to complement them. Unfortunately the size of this volume does not allow for a full account of all the contributions made at the Conference; however, all present were pleased by the number and breadth of those topics covered in the informal afternoon sessions. The purpose of the meeting, as reflected in its title, was to examine the single topic of scattering theory in as many of its manifestations as possible, i.e. as a hub of concepts and techniques from both mathematics and physics. The format of all the topics presented here is mathematical. The physical content embraces classical and quantum mechanical scattering, N-body systems and quantum field theoretical models. Left out are such subjects as the so-called analytic S-matrix theory and phenomeno logical models for high energy scattering. We would like to thank the main lecturers for their excellent presentations and written summaries. They provided a focus for the exceptionally strong interaction among the participants and we hope that some of the coherence achieved is reflected in these published notes. We have made no attempt to unify notation.

Long Time Behaviour of Classical and Quantum Systems

Sandro Graffi,André Martinez
Long Time Behaviour of Classical and Quantum Systems Book PDF

Author : Sandro Graffi,André Martinez
Publisher : World Scientific
Page : 320 pages
File Size : 42,8 Mb
Release : 2001
Category : Science
ISBN : 981279459X

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Long Time Behaviour of Classical and Quantum Systems by Sandro Graffi,André Martinez Pdf

Return to equilibrium in classical and quantum systems / Carlangelo Liverani -- Quantum resonances and trapped trajectories / Johannes Sjostrand -- Return to thermal equilibrium in quantum statistical mechanics / Volker Bach -- Small oscillations in some nonlinear PDE's / Dario Bambusi and Simone Paleari -- The semi-classical Van-Vleck Formula. Application to the Aharonov-Bohm effect / Jean-Marie Bily and Didier Robert -- Fractal dimensions and quantum evolution associated with sparse potential Jacobi matrices / Jean-Michel Combes and Giorgio Mantica -- Infinite step billiards / Mirko Degli Esposti -- Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator / Bernard Helffer and Thierry Ramond -- Asymptotics of scattering poles for two strictly convex obstacles / Mitsuru Ikawa -- Parabolic dynamical systems and inducing / Stefano Isola -- QFT for scalar particles in external fields on Riemannian manifolds / Hiroshi Isozaki -- Existence and born-Oppenheimer Asymptotics of the total scattering cross-section in ion-atom collisions / Thierry Jecko, Markus Klein and Xue Ping Wang -- On asymptotic perturbation theory for quantum mechanics / Gheorghe Nenciu -- Destruction of the beating effect in a periodically driven double-well / Andrea Sacchetti -- Berezin-Toeplitz quantization and Berezin transform / Martin Schlichenmaier.

Long Time Behaviour Of Classical And Quantum Systems - Proceedings Of The Bologna Aptex International Conference

Sandro Graffi,Andre Martinez
Long Time Behaviour Of Classical And Quantum Systems Proceedings Of The Bologna Aptex International Conference Book PDF

Author : Sandro Graffi,Andre Martinez
Publisher : World Scientific
Page : 299 pages
File Size : 47,5 Mb
Release : 2001-04-02
Category : Science
ISBN : 9789814491532

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Long Time Behaviour Of Classical And Quantum Systems - Proceedings Of The Bologna Aptex International Conference by Sandro Graffi,Andre Martinez Pdf

This book is centered on the two minicourses conducted by C Liverani (Rome) and J Sjoestrand (Paris) on the return to equilibrium in classical statistical mechanics and the location of quantum resonances via semiclassical analysis, respectively. The other contributions cover related topics of classical and quantum mechanics, such as scattering theory, classical and quantum statistical mechanics, dynamical localization, quantum chaos, ergodic theory and KAM techniques.

Quantum Theory of Many-Particle Systems

Alexander L. Fetter,John Dirk Walecka
Quantum Theory of Many Particle Systems Book PDF

Author : Alexander L. Fetter,John Dirk Walecka
Publisher : Courier Corporation
Page : 640 pages
File Size : 47,5 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.

Many-Body Schrödinger Equation

Hiroshi Isozaki
Many Body Schr dinger Equation Book PDF

Author : Hiroshi Isozaki
Publisher : Springer Nature
Page : 411 pages
File Size : 41,8 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.

Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular Physics

Donald G. Truhlar,Barry Simon
Multiparticle Quantum Scattering with Applications to Nuclear Atomic and Molecular Physics Book PDF

Author : Donald G. Truhlar,Barry Simon
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461218708

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Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular Physics by Donald G. Truhlar,Barry Simon Pdf

This volume is based on the outcome of a workshop held at the Institute for Mathematics and Its Applications. This institute was founded to promote the interchange of ideas between applied mathematics and the other sciences, and this volume fits into that framework by bringing together the ideas of mathematicians, physicists and chemists in the area of multiparticle scattering theory. The correct formulation of scattering theory for two-body collisions is now well worked out, but systems with three or more particles still present fundamental challenges, both in the formulations of the problem and in the interpretation of computational results. The book begins with two tutorials, one on mathematical issues, including cluster decompositions and asymptotic completeness in N-body quantum systems, and the other on computational approaches to quantum mechanics and time evolution operators, classical action, collisions in laser fields and in magnetic fields, laser-induced processes, barrier resonances, complex dilated expansions, effective potentials for nuclear collisions, long-range potentials, and the Pauli Principle.

Multiparticle Quantum Scattering in Constant Magnetic Fields

Christian Gérard,Izabella Łaba
Multiparticle Quantum Scattering in Constant Magnetic Fields Book PDF

Author : Christian Gérard,Izabella Łaba
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 46,5 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.

Quantum Theory Of Tunneling

Mohsen Razavy
Quantum Theory Of Tunneling Book PDF

Author : Mohsen Razavy
Publisher : World Scientific
Page : 574 pages
File Size : 41,5 Mb
Release : 2003-01-29
Category : Science
ISBN : 9789814488440

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Quantum Theory Of Tunneling by Mohsen Razavy Pdf

This book provides a comprehensive introduction to the theoretical foundations of quantum tunneling, stressing the basic physics underlying the applications. The topics addressed include exponential and nonexponential decay processes and the application of scattering theory to tunneling problems. In addition to the Schrödinger equation approach, the path integral, Heisenberg's equations and the phase space method are all used to study the motion of a particle under the barrier. Extensions to the multidimensional cases and tunneling of particles with internal degrees of freedom are also considered. Furthermore, recent advances concerning time delay and tunneling times and some of the problems associated with their measurement are also discussed. Finally, some examples of tunneling in atomic, molecular, nuclear and condensed matter physics are presented.

Scattering Theory of Waves and Particles

Roger G. Newton
Scattering Theory of Waves and Particles Book PDF

Author : Roger G. Newton
Publisher : Springer
Page : 770 pages
File Size : 53,8 Mb
Release : 1982-07-29
Category : Computers
ISBN : UOM:39015072611919

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Scattering Theory of Waves and Particles by Roger G. Newton Pdf

Appendices, notes, references and problems after each chapter

Quantum Field Theory II: Quantum Electrodynamics

Eberhard Zeidler
Quantum Field Theory II Quantum Electrodynamics Book PDF

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 1125 pages
File Size : 41,5 Mb
Release : 2008-09-03
Category : Mathematics
ISBN : 9783540853770

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Quantum Field Theory II: Quantum Electrodynamics by Eberhard Zeidler Pdf

And God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential source of our knowledge about the physical laws of nature, ranging from the seventeenth century geometrical optics up to the twentieth century theory of general relativity and quantum electrodynamics. Folklore Don’t give us numbers: give us insight! A contemporary natural scientist to a mathematician The present book is the second volume of a comprehensive introduction to themathematicalandphysicalaspectsofmodernquantum?eldtheorywhich comprehends the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics Volume V: The Physics of the Standard Model Volume VI: Quantum Gravitation and String Theory. It is our goal to build a bridge between mathematicians and physicists based on the challenging question about the fundamental forces in • macrocosmos (the universe) and • microcosmos (the world of elementary particles). The six volumes address a broad audience of readers, including both und- graduate and graduate students, as well as experienced scientists who want to become familiar with quantum ?eld theory, which is a fascinating topic in modern mathematics and physics.

Multiparticle Quantum Scattering in Constant Magnetic Fields

Christian Gérard
Multiparticle Quantum Scattering in Constant Magnetic Fields Book PDF

Author : Christian Gérard
Publisher : Unknown
Page : 258 pages
File Size : 54,8 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