Multidimensional Periodic Schrödinger Operator
Perturbation Theory and Applications
1st Edition
Published on 28. March 2015
X, 242 pages
978-3-319-16643-8 (ISBN)
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.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
X, 242 p.
File size
2,95 MB
ISBN-13
978-3-319-16643-8 (9783319166438)
DOI
10.1007/978-3-319-16643-8
Schweitzer Classification
Other editions
New editions
E-Book
08/2019
2nd Edition
Springer
€149.79
Available for download
Additional editions
Book
04/2015
Springer
€139.09
Article exhausted; check for reprint
Content
Preface.- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions.- Constructive Determination of the Spectral Invariants.- Periodic Potential from the Spectral Invariants.- Conclusions.
