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Multidimensional Periodic Schrödinger Operator

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The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given.

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Detail Information

Series Title

Springer Tracts in Modern Physics

Call Number

-

Publisher

: ., 2015

Collation

X, 242

Language

English

ISBN/ISSN

978-3-319-38671-3

Classification

NONE

Content Type

-

Media Type

-

Carrier Type

-

Edition

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Subject(s)

Mathematical Physics
Condensed Matter Physics
Quantum Physics

Specific Detail Info

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Statement of Responsibility

-

Other Information

Cataloger

firdan

Source

-

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