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024 7 $a10.1007/BFb0105531
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035   $a(DE-He213)978-3-540-45170-9
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100   $a20121227d2000      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aScattering Theory: Some Old and New Problems$b[electronic resource] /$fby Dmitri R. Yafaev
205   $a1st ed. 2000.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000.
215   $a1 online resource (XVI, 176 p.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1735
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-67587-6 
320   $aIncludes bibliographical references (pages [155]-166) and index.
327   $aBasic 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.
330   $aScattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1735
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aFunctional analysis
606   $aIntegral equations
606   $aPartial differential equations
606   $aMathematical physics
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aFunctional analysis.
615  0$aIntegral equations.
615  0$aPartial differential equations.
615  0$aMathematical physics.
615 14$aAnalysis.
615 24$aFunctional Analysis.
615 24$aIntegral Equations.
615 24$aPartial Differential Equations.
615 24$aTheoretical, Mathematical and Computational Physics.
676   $a510
686   $a35P25$2msc
686   $a81Uxx$2msc
686   $a47A40$2msc
700   $aYafaev$b Dmitri R$4aut$4http://id.loc.gov/vocabulary/relators/aut$062696
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466504303316
996   $aScattering theory$9262202
997   $aUNISA