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AuthorYafaev, Dmitri R. author
TitleScattering Theory: Some Old and New Problems [electronic resource] / by Dmitri R. Yafaev
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2000
Connect tohttp://dx.doi.org/10.1007/BFb0105531
Descript XVI, 176 p. online resource

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 Schrรถdinger 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 Schrรถdinger 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


CONTENT

Basic concepts -- 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 -- A stationary representation -- The short-range case -- The long-range case -- The relative scattering matrix -- Setting the scattering problem -- Resolvent equations for three-particle systems -- Asymptotic completeness. A sketch of proof -- The scattering matrix and eigenfunctions for multiparticle systems -- New channels of scattering -- The heisenberg model -- Infinite obstacle scattering


Mathematics Mathematical analysis Analysis (Mathematics) Functional analysis Integral equations Partial differential equations Physics Mathematics Analysis Functional Analysis Integral Equations Partial Differential Equations Theoretical Mathematical and Computational Physics



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