Perturbation Theory For Schr Dinger Operators With Complex Potentials
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Topics In The Theory Of Schr Dinger Operators
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Author : Huzihiro Araki
language : en
Publisher: World Scientific
Release Date : 2004
Topics In The Theory Of Schr Dinger Operators written by Huzihiro Araki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Medical categories.
This invaluable book presents reviews of some recent topics in thetheory of SchrAdinger operators. It includes a short introduction tothe subject, a survey of the theory of the SchrAdinger equation whenthe potential depends on the time periodically, an introduction to theso-called FBI transformation (also known as coherent state expansion)with application to the semi-classical limit of the S-matrix, anoverview of inverse spectral and scattering problems, and a study ofthe ground state of the PauliOCoFierz model with the use of thefunctional integral. The material is accessible to graduate studentsand non-expert researchers."
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.
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: 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.
Schr Dinger Operators
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Author : Hans L. Cycon
language : en
Publisher: Springer
Release Date : 2009-08-19
Schr Dinger Operators written by Hans L. Cycon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-19 with Science categories.
A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem.
Perturbation Methods With Applications In Science And Engineering
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Author : İlkay Bakırtaş
language : en
Publisher: BoD – Books on Demand
Release Date : 2018-10-17
Perturbation Methods With Applications In Science And Engineering written by İlkay Bakırtaş and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-17 with Mathematics categories.
The governing equations of mathematical, chemical, biological, mechanical and economical models are often nonlinear and too complex to be solved analytically. Perturbation theory provides effective tools for obtaining approximate analytical solutions to a wide variety of such nonlinear problems, which may include differential or difference equations. In this book, we aim to present the recent developments and applications of the perturbation theory for treating problems in applied mathematics, physics and engineering. The eight chapters cover a variety of topics related to perturbation methods. The book is intended to draw attention of researchers and scientist in academia and industry.
Schr Dinger Operators
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Author : Hans L. Cycon
language : en
Publisher: Springer Science & Business Media
Release Date : 1987
Schr Dinger Operators written by Hans L. Cycon 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 1987 with Computers categories.
Are you looking for a concise summary of the theory of Schrödinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don’t just cover general properties, but also detail multiparticle quantum mechanics – including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years.
Multidimensional Periodic Schr Dinger Operator
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Author : Oktay Veliev
language : en
Publisher: Springer
Release Date : 2019-08-02
Multidimensional Periodic Schr Dinger Operator written by Oktay Veliev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-02 with Science categories.
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.
Gaps In The Dispersion Relation Of The One Dimensional Schr Dinger Operator With Periodic Potentials
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Author : Thomas Z. Dean
language : en
Publisher:
Release Date : 2022
Gaps In The Dispersion Relation Of The One Dimensional Schr Dinger Operator With Periodic Potentials written by Thomas Z. Dean and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Schrödinger operator categories.
The self-adjoint Schrödinger operator is the difference of a kinetic (Laplacian operator)and potential energy (multiplication operator). The study of this operator continues to attract the interest of many mathematicians and physicists. A commonly used mathematical approach to understand quantum mechanics is through the use of spectral and perturbation theory of the Schrödinger operator. By understanding the spectrum of the Schrödinger operator, we can understand the allowed energy states of a quantum system corresponding to a specific potential. The choice of potential dictates the behavior of the spectrum of the Schrödinger operator which in return provides insight into the behavior of the corresponding quantum system. We study periodic potentials for the Schrödinger operator because of its relation to the phenomena of Anderson localization and semi-conductor theory. A new algorithm is developed to numerically approximate the spectrum of one-dimensional periodic Schrödinger operators. From this, the behavior of spectral gaps are understood when parameters of the potential are changed (e.g. period and amplitude).Moreover, the convergence properties and the behavior of the spectrum as continuous periodic potentials are approximated by their Fourier modes are studied. The behavior of the first spectral gap for such convergences are demonstrated. These results show that the first spectral gap is well-behaved in the strong and norm resolvent convergence.