Perturbation Theory for the Schrödinger Operator with a Periodic Potential / Edition 1

Perturbation Theory for the Schrödinger Operator with a Periodic Potential / Edition 1

by Yulia E. Karpeshina
     
 

ISBN-10: 3540631364

ISBN-13: 9783540631361

Pub. Date: 09/19/1997

Publisher: Springer Berlin Heidelberg

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

Overview

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.

Product Details

ISBN-13:
9783540631361
Publisher:
Springer Berlin Heidelberg
Publication date:
09/19/1997
Series:
Lecture Notes in Mathematics Series, #1663
Edition description:
1997
Pages:
359
Product dimensions:
9.21(w) x 6.14(h) x 0.75(d)

Table of Contents

Perturbation theory for a polyharmonic operator in the case of 2>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.

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