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Scattering theory : some old and new problems / Dimitri Yafaev.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1735.Publication details: Berlin ; New York : Springer, ©2000.Description: 1 online resource (xvi, 169 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540451709
  • 3540451706
Subject(s): Additional physical formats: Print version:: Scattering theory : some old and new problemsDDC classification:
  • 515.353 22
LOC classification:
  • QA3 .L28 no. 1735
Online resources:
Contents:
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.
Summary: 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 Schrdinger 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 Schrdinger 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.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library eBook LN Mathematic Available
Total holds: 0

Includes bibliographical references (pages 155-166) and index.

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.

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 Schrdinger 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 Schrdinger 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.

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