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Perturbation theory for Schroedinger operator with periodic potential

Обложка книги Perturbation theory for Schroedinger operator with periodic potential

Perturbation theory for Schroedinger operator with periodic potential

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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