Perturbation Theory for the Schrödinger Operator with a Periodic Potential. 1st ed. 1997

種類:

電子ブック

責任表示:

by Yulia E. Karpeshina

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997

著者名:

• Karpeshina, Yulia E.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1663

ISBN:

9783540691563 [3540691561]    

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.

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