000 | 03670nam a22005415i 4500 | ||
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001 | 978-3-540-45170-9 | ||
003 | DE-He213 | ||
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007 | cr nn 008mamaa | ||
008 | 121227s2000 gw | s |||| 0|eng d | ||
020 |
_a9783540451709 _9978-3-540-45170-9 |
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024 | 7 |
_a10.1007/BFb0105531 _2doi |
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050 | 4 | _aQA299.6-433 | |
072 | 7 |
_aPBK _2bicssc |
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_aMAT034000 _2bisacsh |
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072 | 7 |
_aPBK _2thema |
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_a515 _223 |
100 | 1 |
_aYafaev, Dmitri R. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aScattering Theory: Some Old and New Problems _h[electronic resource] / _cby Dmitri R. Yafaev. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2000. |
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300 |
_aXVI, 176 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1735 |
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505 | 0 | _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. | |
520 | _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. | ||
650 | 0 | _aGlobal analysis (Mathematics). | |
650 | 0 | _aFunctional analysis. | |
650 | 0 | _aIntegral equations. | |
650 | 0 | _aDifferential equations, partial. | |
650 | 1 | 4 |
_aAnalysis. _0http://scigraph.springernature.com/things/product-market-codes/M12007 |
650 | 2 | 4 |
_aFunctional Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M12066 |
650 | 2 | 4 |
_aIntegral Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12090 |
650 | 2 | 4 |
_aPartial Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12155 |
650 | 2 | 4 |
_aTheoretical, Mathematical and Computational Physics. _0http://scigraph.springernature.com/things/product-market-codes/P19005 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662205273 |
776 | 0 | 8 |
_iPrinted edition: _z9783540675877 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1735 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0105531 |
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912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
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