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Perturbation theory for the Schrödinger operator with a periodic potential
1 online resource (vii, 352 pages) : illustrations.
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.
Introduction -- Perturbation Theory for a Polyharmonic Operator in the Case of 2l> n -- Perturbation Theory for the Polyharmonic Operator in the Case of 4l>n+1 -- Perturbation Theory for Schrdinger Operator with a Periodic Potential -- The Interaction of a Free Wave with a Semi- bounded Crystal -- References -- Index.
Includes bibliographical references (pages [339]-349) and index.
Lecture notes in mathematics (Springer-Verlag) ; 1663