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Field name	Details
Dewey Class	515
Title	Scattering Theory: Some Old and New Problems ([EBook] /) / by Dmitri R. Yafaev.
Author	Yafaev, Dmitri R.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2000.
Physical Details	XVI, 176 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1735
ISBN	9783540451709
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0105531
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Functional Analysis . Integral Equations . Mathematical analysis . Mathematics . Partial differential equations . Physics . Theoretical, Mathematical and Computational Physics . Authors: Yafaev, Dmitri R. . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 515 .

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Scattering Theory: Some Old and New Problems

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