Scattering Theory of Classical and Quantum N-Particle Systems PDF Download
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Author: Jan Derezinski
Publisher: Springer
ISBN: 9783642082849
Category : Science
Languages : en
Pages : 444
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Book Description
A system of N non-relativistic classical particles interacting with pair potentials is described by a Hamiltonian of the form (0.0.1) This Hamiltonian generates a flow ¢(t) on the phase space JR3N x JR3N. An analogous system of N quantum particles is described by a Hamiltonian of the form N 1 H := -L -Llj + L \lij(Xi - Xj)' (0.0.2) j=l 2mj l$i
Author: Jan Derezinski
Publisher: Springer
ISBN: 9783642082849
Category : Science
Languages : en
Pages : 444
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Book Description
A system of N non-relativistic classical particles interacting with pair potentials is described by a Hamiltonian of the form (0.0.1) This Hamiltonian generates a flow ¢(t) on the phase space JR3N x JR3N. An analogous system of N quantum particles is described by a Hamiltonian of the form N 1 H := -L -Llj + L \lij(Xi - Xj)' (0.0.2) j=l 2mj l$i
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: Harald Friedrich
Publisher: Springer
ISBN: 3662485265
Category : Science
Languages : en
Pages : 293
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Book Description
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Author: Dmitri R. Yafaev
Publisher: Springer
ISBN: 3540451706
Category : Mathematics
Languages : en
Pages : 185
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Book Description
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: Huzihiro Araki
Publisher: World Scientific
ISBN: 9812387978
Category : Science
Languages : en
Pages : 288
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Book Description
This invaluable book presents reviews of some recent topics in the theory of Schrdinger operators. It includes a short introduction to the subject, a survey of the theory of the Schrdinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion) with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli-Fierz model with the use of the functional integral. The material is accessible to graduate students and non-expert researchers.
Author: Nikolai Chernov
Publisher: American Mathematical Soc.
ISBN: 0821838407
Category : Mathematics
Languages : en
Pages : 354
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Book Description
Surveys topics in differential equations that are associated with mathematical physics. This book includes such topics as asymptotic formulas for the ground-state energy of fermionic gas, $J$-self adjoint Dirac operators, and spectral theory of Schrodinger operators. It is suitable for mathematicians and physicists.
Author: Michael Ruzhansky
Publisher: Springer Science & Business Media
ISBN: 3034804547
Category : Mathematics
Languages : en
Pages : 327
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Book Description
Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area.
Author: David Ellwood
Publisher: American Mathematical Soc.
ISBN: 0821868616
Category : Mathematics
Languages : en
Pages : 587
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Book Description
This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author: Monique Combescure
Publisher: Springer Science & Business Media
ISBN: 9400701950
Category : Mathematics
Languages : en
Pages : 419
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Book Description
This book presents the various types of coherent states introduced and studied in the physics and mathematics literature and describes their properties together with application to quantum physics problems. It is intended to serve as a compendium on coherent states and their applications for physicists and mathematicians, stretching from the basic mathematical structures of generalized coherent states in the sense of Perelomov via the semiclassical evolution of coherent states to various specific examples of coherent states (hydrogen atom, quantum oscillator, ...).
Author: József Lörinczi
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110389932
Category : Mathematics
Languages : en
Pages : 593
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Book Description
This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. The first volume concentrates on Feynman-Kac-type formulae and Gibbs measures.
