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Scattering Theory: Some Old and New Problems

Some Old and New Problems
 Taschenbuch
Besorgungstitel | Lieferzeit:3-5 Tage I
ISBN-13:
9783540675877
Einband:
Taschenbuch
Seiten:
176
Autor:
Dmitri R. Yafaev
Gewicht:
304 g
Format:
236x156x13 mm
Serie:
Vol.1735, Lecture Notes in Mathematics
Sprache:
Deutsch
Beschreibung:

From the 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
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. We construct also potentials for which asymptotic completeness is violated. 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.

From the 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
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. We construct also potentials for which asymptotic completeness is violated. 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.
Autor: Dmitri R. Yafaev
ISBN-13:: 9783540675877
ISBN: 3540675876
Verlag: Springer, Berlin
Gewicht: 304g
Seiten: 176
Sprache: Deutsch
Sonstiges: Taschenbuch, 236x156x13 mm, XVI, 176 p.