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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 :2019.
Description:	xii, 326 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Schrodinger operator.
Online resource:	https://doi.org/10.1007/978-3-030-24578-8
ISBN:	9783030245788$q(electronic bk.)

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

Multidimensional periodic Schrodinger operatorperturbation theory and applications /[electronic resource] :by Oktay Veliev. - 2nd ed. - Cham :Springer International Publishing :2019. - xii, 326 p. :ill., digital ;24 cm.

Chapter 1 - Preliminary Facts -- Chapter 2- From One-dimensional to Multidimensional -- Chapter 3 - Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions.-Chapter 4 -Constructive Determination of the Spectral Invariants -- Chapter 5 - Periodic Potential from the Spectral Invariants -- Chapter 6 - Conclusions.

This book describes the direct and inverse problems of the multidimensional Schrodinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential. This updated second edition includes an additional chapter that specifically focuses on lower-dimensional cases, providing the basis for the higher-dimensional considerations of the chapters that follow.

ISBN: 9783030245788$q(electronic bk.)

Standard No.: 10.1007/978-3-030-24578-8doiSubjects--Topical Terms:

275658
Schrodinger operator.

LC Class. No.: QC174.17.S3 / V455 2019

Dewey Class. No.: 530.124

Multidimensional periodic Schrodinger operatorperturbation theory and applications /
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245 1 0 $a Multidimensional periodic Schrodinger operator $h [electronic resource] : $b perturbation theory and applications / $c by Oktay Veliev.
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300 $a xii, 326 p. : $b ill., digital ; $c 24 cm.
505 0 $a Chapter 1 - Preliminary Facts -- Chapter 2- From One-dimensional to Multidimensional -- Chapter 3 - Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions.-Chapter 4 -Constructive Determination of the Spectral Invariants -- Chapter 5 - Periodic Potential from the Spectral Invariants -- Chapter 6 - Conclusions.
520 $a This book describes the direct and inverse problems of the multidimensional Schrodinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential. This updated second edition includes an additional chapter that specifically focuses on lower-dimensional cases, providing the basis for the higher-dimensional considerations of the chapters that follow.
650 0 $a Schrodinger operator. $3 275658
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