Perturbation theory for the Schrödinger operator with a periodic potential
著者
書誌事項
Perturbation theory for the Schrödinger operator with a periodic potential
（Lecture notes in mathematics, 1663）
Springer-Verlag, c1997
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注記
Includes bibliographical references (p. [339]-349) and index (p. [351]-352)
内容説明・目次
内容説明
The book is devoted to perturbation theory for the Schroedinger 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 Schroedinger 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.
目次
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 Schroedinger operator with a periodic potential.- The interaction of a free wave with a semi-bounded crystal.
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