Multidimensional Periodic Schrödinger Operator

Perturbation Theory and Applications

By:

Oktay Veliev

Format:

Paperback / softback

Series:

Springer Tracts in Modern Physics

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Description

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.

Release date NZ

October 9th, 2016

Author

Oktay Veliev

Series

Springer Tracts in Modern Physics

Pages

242

Edition

Softcover reprint of the original 1st ed. 2015

Audience

Professional & Vocational

Illustrations

X, 242 p.

Dimensions

155x235x13

ISBN-13

9783319386713

Product ID

26138623

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