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 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expository material, research work previously available only in the form of journal articles, as well as some new unpublished results.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 and largely self-contained, and the text is carefully written with attention to detail.

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 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 ex 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 Min 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.

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 Mathematics 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.

Combinatorial Geometry And Its Algorithmic Applications

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Author : János Pach
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Combinatorial Geometry And Its Algorithmic Applications written by János Pach 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.

"Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. "Combinatorial Geometry and Its Algorithmic Applications" is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography."--BOOK JACKET.

Trace Ideals And Their Applications

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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Trace Ideals And Their Applications written by Barry Simon 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 2005 with Mathematics categories.

From a review of the first edition: Beautifully written and well organized ... indispensable for those interested in certain areas of mathematical physics ... for the expert and beginner alike. The author deserves to be congratulated both for his work in unifying a subject and for showing workers in the field new directions for future development. --Zentralblatt MATH This is a second edition of a well-known book on the theory of trace ideals in the algebra of operators in a Hilbert space. Because of the theory's many different applications, the book was widely used and much in demand. For this second edition, the author has added four chapters on the closely related theory of rank one perturbations of self-adjoint operators. He has also included a comprehensive index and an addendum describing some developments since the original notes were published. This book continues to be a vital source of information for those interested in the theory of trace ideals and in its applications to various areas of mathematical physics.

Arithmetic Differential Equations

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Author : Alexandru Buium
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Arithmetic Differential Equations written by Alexandru Buium 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 2005 with Mathematics categories.

For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.

Sturm Liouville Theory

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Author : Anton Zettl
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Sturm Liouville Theory written by Anton Zettl 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 2005 with Education categories.

In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed. An extensive list of references and examples is provided and numerous open problems are given. The list of examples includes those classical equations and functions associated with the names of Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, Morse, as well as examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.

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.

Journal Of Mathematical Sciences The University Of Tokyo

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Author :
language : en
Publisher:
Release Date : 2001

Journal Of Mathematical Sciences The University Of Tokyo written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

Finite Dimensional Algebras And Quantum Groups

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Author : Bangming Deng
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Finite Dimensional Algebras And Quantum Groups written by Bangming Deng 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 2008 with Mathematics categories.

"The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.