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Multidimensional Periodic Schrödinger Operator = Perturbation Theory and Applications /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Multidimensional Periodic Schrödinger Operator/ by Oktay Veliev.
Reminder of title:	Perturbation Theory and Applications /
Author:	Veliev, Oktay.
Description:	XII, 326 p. 4 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Quantum physics. -
Online resource:	https://doi.org/10.1007/978-3-030-24578-8
ISBN:	9783030245788

Multidimensional Periodic Schrödinger Operator = Perturbation Theory and Applications /
Veliev, Oktay.

Multidimensional Periodic Schrödinger OperatorPerturbation Theory and Applications /[electronic resource] :by Oktay Veliev. - 2nd ed. 2019. - XII, 326 p. 4 illus.online resource.

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 Schrödinger 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:

1179090
Quantum physics.

LC Class. No.: QC173.96-174.52

Dewey Class. No.: 530.12

Multidimensional Periodic Schrödinger Operator = Perturbation Theory and Applications /
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520 $a This book describes the direct and inverse problems of the multidimensional Schrödinger 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.
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