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Lecture Notes in Mathematics : Lecture Notes in Mathematics - Yulia E. Karpeshina

Lecture Notes in Mathematics

By: Yulia E. Karpeshina

Paperback | 19 August 1997

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The book is devoted to perturbation theory for the Schr¶dinger 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 Schr¶dinger 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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