Overview

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.

Full Product Details

Author:   Dmitri R. Yafaev
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2000 ed.
Volume:   1735
Dimensions:   Width: 21.60cm , Height: 1.00cm , Length: 27.90cm
Weight:   0.630kg
ISBN:  

9783540675877

ISBN 10:   3540675876
Pages:   176
Publication Date:   26 June 2000
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Part 1. The Schroedinger operator of two-particle systems 1. Basic notions 2. Short-range interactions. Asymptotic completeness 3. Short-range interactions. Miscellaneous 4. Long-range interactions. The scheme of smooth perturbations 5. The generalized Fourier transform 6. Long-range matrix potentials Part 2. The scattering matrix 7. A stationary representarion 8. The short-range case 9. The long-range cas 10. The relative scattering matrix Part 3. The multiparticle Schroedinger operator and related problems 11. Setting the scattering problem 12. Resolvent equations 13. Asymptotic completeness. A sketch of proof 14. The scattering matrix for multiparticle systems 15. New channels of scattering 16. The Heisenberg model 17. Infinite obstacle scattering

Reviews

“This book provides a modern survey of important problems of the mathematical scattering theory. … The book fills a gap in the literature because it emphasizes the stationary approach to the scattering theory problems.” (Michael Perelmuter, zbMATH 0951.35003, 2022)

This book provides a modern survey of important problems of the mathematical scattering theory. ... The book fills a gap in the literature because it emphasizes the stationary approach to the scattering theory problems. (Michael Perelmuter, zbMATH 0951.35003, 2022)

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