ENGLISH

Perturbation Theory for the Schrödinger Operator with a Periodic Potential

By Yulia E. Karpeshina (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1997
ISBN
3540631364, 9783540631361
DOI
10.1007/BFb0094264
LCC
QA3 .L28 no. 1663
Open Library ID
OL676002M
Language
english
Format
DJVU
Filesize
2 MB (2446974 bytes)
Series
Lecture Notes in Mathematics 1663
Edition
1
Pages
356\357
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Partial Differential Equations;Mathematical and Co

Description

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.

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