Multiparticle Quantum Scattering In Constant Magnetic Fields
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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expository material, research work previously available only in the form of journal articles, as well as some new unpublished results.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.
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
Schr Dinger Operators
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Author : Hans L. Cycon
language : en
Publisher: Springer Science & Business Media
Release Date : 1987
Schr Dinger Operators written by Hans L. Cycon 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 1987 with Computers categories.
Are you looking for a concise summary of the theory of Schrödinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don’t just cover general properties, but also detail multiparticle quantum mechanics – including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years.
Multiparticle Quantum Scattering With Applications To Nuclear Atomic And Molecular Physics
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Author : Donald G. Truhlar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multiparticle Quantum Scattering With Applications To Nuclear Atomic And Molecular Physics written by Donald G. Truhlar 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 2012-12-06 with Mathematics categories.
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 With Applications To Nuclear Atomic And Molecular Physics
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Author : Donald G. Truhlar
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Multiparticle Quantum Scattering With Applications To Nuclear Atomic And Molecular Physics written by Donald G. Truhlar 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 with Mathematics categories.
This IMA Volume in Mathematics and its Applications MULTIPARTICLE QUANTUM SCATTERING WITH APPLICATIONS TO NUCLEAR, ATOMIC AND MOLECULAR PHYSICS is based on the proceedings of a workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Donald G. Truhlar and Barry Simon for their exƯ cellent work as organizers of this meeting and as editors of the proceedings. We also take this opportunity to thank the National Science Foundation (NSF), the Army Research Office (ARO), and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The workshop on Multiparticle Quantum Scattering with Applications to Nuclear, Atomic, and Molecular Physics was held June 12-16, 1995 at the Institute for Mathematics and Its Applications in the University of MinƯ nesota Twin Cities campus as part of the 1994-95 Program on Waves and Scattering. There were about seventy participants including the plenary lecturers whose contributions are included in this volume. The workshop was preceded by a two-day tutorial featuring lectures by Donald J. Kouri and Gian Michele Graf, and we are pleased that both Professors Graf and Kouri were able to write up their tutorials as opening chapters of this volume
Schr Dinger Operators
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Author : Hans L. Cycon
language : en
Publisher: Springer
Release Date : 2009-08-19
Schr Dinger Operators written by Hans L. Cycon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-19 with Science categories.
A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem.
Spectral Theory And Mathematical Physics A Festschrift In Honor Of Barry Simon S 60th Birthday
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Author : Fritz Gesztesy
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Spectral Theory And Mathematical Physics A Festschrift In Honor Of Barry Simon S 60th Birthday written by Fritz Gesztesy 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 2007 with Mathematical physics categories.
This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to aparticular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random andErgodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensiveintroduction into an area covered in this volume.
Spectral And Scattering Theory For Quantum Magnetic Systems
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Author : Philippe Briet
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Spectral And Scattering Theory For Quantum Magnetic Systems written by Philippe Briet 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 2009 with Mathematics categories.
Contains the proceedings of the conference on Spectral and Scattering Theory for Quantum Magnetic Systems, which took place at CIRM, Luminy, France, in July 2008. This volume includes original results presented by some of the invited speakers and surveys on advances in the mathematical theory of quantum magnetic Hamiltonians.
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.
Mathematical Concepts Of Quantum Mechanics
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Author : Stephen J. Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Mathematical Concepts Of Quantum Mechanics written by Stephen J. Gustafson 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 2003 with Education categories.
The book gives a streamlined introduction to quantum mechanics, while describing the basic mathematical structures underpinning this discipline. Starting with an overview of the key physical experiments illustrating the origin of the physical foundations, the book proceeds to a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The topics presented include spectral theory, many-body theory, positive temperatures, path integrals and quasiclassical asymptotics, the theory of resonances, an introduction to quantum field theory and the theory of radiation. The book can serve as a text for an intermediate course in quantum mechanics, or a more advanced topics course.