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- catalog abstract "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.".
- catalog contributor b11756476.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description "Includes bibliographical references and index.".
- catalog description "Part 1. The Schroedinger operator of two-particle systems: Basic notions -- Short-range interactions -- Asymptotic completeness -- Short-range interactions. Miscellaneous -- Long-range interactions. The scheme of smooth perturbations -- The generalized Fourier transform -- Long-range matrix potentials -- Part 2. The scattering matrix: A stationary representation -- The short-range case -- The long-range case -- The relative scattering matrix -- Part 3. The multiparticle Schroedinger operator and related problems: Setting the scattering problem -- Resolvent equations -- Asymptotic completeness -- A sketch of proof -- The scattering matrix for multiparticle systems -- New channels of scattering -- The Heisenberg model -- Infinite obstacle scattering.".
- catalog 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.".
- catalog extent "xvi, 169 p. :".
- catalog identifier "3540675876 (softcover)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1735.".
- catalog isPartOf "Lecture notes in mathematics ; 1735".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "510 s 515/.353 21".
- catalog subject "Differential equations, partial.".
- catalog subject "Mathematical physics.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1735 QA377".
- catalog subject "Scattering (Mathematics)".
- catalog tableOfContents "Part 1. The Schroedinger operator of two-particle systems: Basic notions -- Short-range interactions -- Asymptotic completeness -- Short-range interactions. Miscellaneous -- Long-range interactions. The scheme of smooth perturbations -- The generalized Fourier transform -- Long-range matrix potentials -- Part 2. The scattering matrix: A stationary representation -- The short-range case -- The long-range case -- The relative scattering matrix -- Part 3. The multiparticle Schroedinger operator and related problems: Setting the scattering problem -- Resolvent equations -- Asymptotic completeness -- A sketch of proof -- The scattering matrix for multiparticle systems -- New channels of scattering -- The Heisenberg model -- Infinite obstacle scattering.".
- catalog title "Scattering theory : some old and new problems / Dimitri Yafaev.".
- catalog type "text".