Perturbation Theory for the Schrödinger Operator with a Periodic Potential [electronic resource] / by Yulia E. Karpeshina.

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.