The book is devoted to perturbation theory for the Schrdinger 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 Schrdinger 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.

1. Introduction 2. Perturbation Theory for a Polyharmonic Operator in the Case of 2l>n 3. Perturbation Theory for the Polyharmonic Operator in the Case 4l>n+1 4. Perturbation Theory for Schrodinger Operator with a Periodic Potential 5. The Interaction of a Free Wave with a Semi-bounded Crystal

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