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Multidimensional periodic Schrodinger operatorperturbation theory and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Multidimensional periodic Schrodinger operatorby Oktay Veliev.
Reminder of title:	perturbation theory and applications /
Author:	Veliev, Oktay.
Published:	Cham :Springer International Publishing :2015.
Description:	x, 242 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Schrodinger operator.
Online resource:	http://dx.doi.org/10.1007/978-3-319-16643-8
ISBN:	9783319166438 (electronic bk.)

Multidimensional periodic Schrodinger operatorperturbation theory and applications /
Veliev, Oktay.

Multidimensional periodic Schrodinger operatorperturbation theory and applications /[electronic resource] :by Oktay Veliev. - Cham :Springer International Publishing :2015. - x, 242 p. :ill., digital ;24 cm. - Springer tracts in modern physics,v.2630081-3869 ;. - Springer tracts in modern physics ;168..

Preface -- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- Constructive Determination of the Spectral Invariants -- Periodic Potential from the Spectral Invariants -- Conclusions.

The book describes the direct problems and the inverse problem of the multidimensional Schrodinger 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.

ISBN: 9783319166438 (electronic bk.)

Standard No.: 10.1007/978-3-319-16643-8doiSubjects--Topical Terms:

275658
Schrodinger operator.

LC Class. No.: QC174.17.S3

Dewey Class. No.: 530.124

Multidimensional periodic Schrodinger operatorperturbation theory and applications /
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100 1 $a Veliev, Oktay. $3 716111
245 1 0 $a Multidimensional periodic Schrodinger operator $h [electronic resource] : $b perturbation theory and applications / $c by Oktay Veliev.
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520 $a The book describes the direct problems and the inverse problem of the multidimensional Schrodinger 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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