Perturbation Theory For The Schr Dinger Operator With A Periodic Potential
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Perturbation Theory For The Schr Dinger Operator With A Periodic Potential
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Author : Yulia E. Karpeshina
language : en
Publisher: Springer
Release Date : 2006-11-14
Perturbation Theory For The Schr Dinger Operator With A Periodic Potential written by Yulia E. Karpeshina and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The book is devoted to perturbation theory for the Schrödinger operator with a periodic potential, describing motion of a particle in bulk matter. The Bloch eigenvalues of the operator are densely situated in a high energy region, so regular perturbation theory is ineffective. The mathematical difficulties have a physical nature - a complicated picture of diffraction inside the crystal. The author develops a new mathematical approach to this problem. It provides mathematical physicists with important results for this operator and a new technique that can be effective for other problems. The semiperiodic Schrödinger operator, describing a crystal with a surface, is studied. Solid-body theory specialists can find asymptotic formulae, which are necessary for calculating many physical values.
Perturbation Theory For The Schrodinger Operator With A Periodic Potential
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Author : Yulia E. Karpeshina
language : en
Publisher:
Release Date : 2014-01-15
Perturbation Theory For The Schrodinger Operator With A Periodic Potential written by Yulia E. Karpeshina and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Multidimensional Periodic Schr Dinger Operator
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Author : Oktay Veliev
language : en
Publisher:
Release Date : 2015
Multidimensional Periodic Schr Dinger Operator written by Oktay Veliev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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.
Multidimensional Periodic Schr Dinger Operator
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Author : Oktay Veliev
language : en
Publisher: Springer Nature
Release Date :
Multidimensional Periodic Schr Dinger Operator written by Oktay Veliev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Introduction To Quantum Mechanics
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Author : H. J. W. Mller-Kirsten
language : en
Publisher: World Scientific
Release Date : 2006
Introduction To Quantum Mechanics written by H. J. W. Mller-Kirsten and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schrdinger equation on the one hand and the applications of the path integral on the other. Different from traditional texts and using a systematic perturbation method, the solution of Schrdinger equations includes also those with anharmonic oscillator potentials, periodic potentials, screened Coulomb potentials and a typical singular potential, as well as the investigation of the large order behavior of the perturbation series. On the path integral side, after introduction of the basic ideas, the expansion around classical configurations in Euclidean time, such as instantons, is considered, and the method is applied in particular to anharmonic oscillator and periodic potentials. Numerous other aspects are treated on the way, thus providing the reader an instructive overview over diverse quantum mechanical phenomena, e.g. many other potentials, Green's functions, comparison with WKB, calculation of lifetimes and sojourn times, derivation of generating functions, the Coulomb problem in various coordinates, etc. All calculations are given in detail, so that the reader can follow every step.
Perturbation Theory In Periodic Problems For Two Dimensional Integrable Systems
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Author : I. M. Krichever
language : en
Publisher: CRC Press
Release Date : 1992
Perturbation Theory In Periodic Problems For Two Dimensional Integrable Systems written by I. M. Krichever and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
The Operator Formalism In Quantum Perturbation Theory
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Author : Bryce S. DeWitt
language : en
Publisher:
Release Date : 1955
The Operator Formalism In Quantum Perturbation Theory written by Bryce S. DeWitt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with categories.
Perturbation Theory For Schr Dinger Operators With Complex Potentials
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Author : Emanuela Beatrice Caliceti
language : en
Publisher:
Release Date : 1983
Perturbation Theory For Schr Dinger Operators With Complex Potentials written by Emanuela Beatrice Caliceti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Schrödinger operator categories.
Adiabatic Perturbation Theory In Quantum Dynamics
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Author : Stefan Teufel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Adiabatic Perturbation Theory In Quantum Dynamics written by Stefan Teufel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Perturbation (Quantum dynamics) categories.
Lecture Notes On Schr Dinger Equations
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Author : Aleksandr Andreevich Pankov
language : en
Publisher:
Release Date : 2007
Lecture Notes On Schr Dinger Equations written by Aleksandr Andreevich Pankov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Combinatorial analysis categories.
CONTENTS: Preface; A Bit of Quantum Mechanics; Operators in Hilbert Spaces; Spectral Theorem for Self-adjoint Operators; Compact Operators and the Hilbert-Schmidt Theorem; Elements of Perturbation Theory; Variational Principles; One-Dimensional Schrödinger Operator; Multidimensional Schrödinger Operator; Periodic Schrödinger Operator; Quantum Graphs; Non-linear Schrödinger Equation; References; Index.