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.

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“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)

Bibliographic Information

Book Title: Scattering Theory: Some Old and New Problems
Authors: Dmitri R. Yafaev
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0105531
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2000
Softcover ISBN: 978-3-540-67587-7Published: 26 June 2000
eBook ISBN: 978-3-540-45170-9Published: 06 May 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVI, 176
Topics: Analysis, Functional Analysis, Integral Equations, Partial Differential Equations, Theoretical, Mathematical and Computational Physics

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Table of contents (17 chapters)

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