Perturbation Theory for the Schrödinger Operator with a Periodic Potential

Yulia E. Karpeshina (auth.)3540631364, 9783540631361

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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Table of contents :
Introduction….Pages 1-22
Perturbation theory for a polyharmonic operator in the case of 2l>n ….Pages 23-62
Perturbation theory for the polyharmonic operator in the case 4l>n+1 ….Pages 63-97
Perturbation theory for Schrödinger operator with a periodic potential….Pages 99-232
The interaction of a free wave with a semi-bounded crystal….Pages 233-338