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＜電子ブック＞
Perturbation Theory for the Schrödinger Operator with a Periodic Potential / by Yulia E. Karpeshina
(Lecture Notes in Mathematics. ISSN:16179692 ; 1663)

版	1st ed. 1997.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1997
本文言語	英語
大きさ	CCCLXIV, 356 p : online resource
著者標目	*Karpeshina, Yulia E author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical physics FREE:Differential Equations FREE:Theoretical, Mathematical and Computational Physics
一般注記	Perturbation theory for a polyharmonic operator in the case of 2l>n -- Perturbation theory for the polyharmonic operator in the case 4l>n+1 -- Perturbation theory for Schrödinger operator with a periodic potential -- The interaction of a free wave with a semi-bounded crystal The book is devoted to perturbation theory for the Schrödinger operator with a periodic potential, describing motion of a particle in bulk matter. The Bloch eigenvalues of the operator are densely situated in a high energy region, so regular perturbation theory is ineffective. The mathematical difficulties have a physical nature - a complicated picture of diffraction inside the crystal. The author develops a new mathematical approach to this problem. It provides mathematical physicists with important results for this operator and a new technique that can be effective for other problems. The semiperiodic Schrödinger operator, describing a crystal with a surface, is studied. Solid-body theory specialists can find asymptotic formulae, which are necessary for calculating many physical values HTTP:URL=https://doi.org/10.1007/BFb0094264

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