國立虎尾科技大學 |

Multidimensional periodic Schrodinger operator = perturbation theory and applications /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Multidimensional periodic Schrodinger operator/ by 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

Multidimensional periodic Schrodinger operator = perturbation 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

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

678114
Schrodinger operator.

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

Dewey Class. No.: 530.124

Multidimensional periodic Schrodinger operator = perturbation theory and applications /
LDR:02660nam a2200337 a 4500 001 942129
003 DE-He213
005 20191213105807.0
006 m d
007 cr nn 008maaau
008 200417s2019 gw s 0 eng d
020 $a 9783030245788 $q (electronic bk.)
020 $a 9783030245771 $q (paper)
024 7 $a 10.1007/978-3-030-24578-8 $2 doi
035 $a 978-3-030-24578-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QC174.17.S3 $b V455 2019
072 7 $a PHQ $2 bicssc
072 7 $a SCI057000 $2 bisacsh
072 7 $a PHQ $2 thema
082 0 4 $a 530.124 $2 23
090 $a QC174.17.S3 $b V437 2019
100 1 $a Veliev, Oktay. $3 1229773
245 1 0 $a Multidimensional periodic Schrodinger operator $h [electronic resource] : $b perturbation theory and applications / $c by Oktay Veliev.
250 $a 2nd ed.
260 $a Cham : $c 2019. $b Springer International Publishing : $b Imprint: Springer,
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 678114
650 0 $a Perturbation (Mathematics) $3 528258
650 0 $a Spectral theory (Mathematics) $3 527757
650 1 4 $a Quantum Physics. $3 671960
650 2 4 $a Solid State Physics. $3 768851
650 2 4 $a Mathematical Physics. $3 786661
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-24578-8
950 $a Physics and Astronomy (Springer-11651)