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Scattering Theory: Some Old and New Problems / by Dmitri R. Yafaev
(Lecture Notes in Mathematics. ISSN:16179692 ; 1735)
版 | 1st ed. 2000. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 2000 |
本文言語 | 英語 |
大きさ | XVI, 176 p : online resource |
著者標目 | *Yafaev, Dmitri R author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Functional analysis LCSH:Integral equations LCSH:Differential equations LCSH:Mathematical physics FREE:Analysis FREE:Functional Analysis FREE:Integral Equations FREE:Differential Equations FREE:Theoretical, Mathematical and Computational Physics |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/BFb0105531 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783540451709 |
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EB00235849 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000109137 |
ISBN | 9783540451709 |
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