Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators
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Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators
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Author : M. M. Skriganov
language : en
Publisher: American Mathematical Soc.
Release Date : 1987
Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators written by M. M. Skriganov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators
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Author : Maksim M. Skriganov
language : en
Publisher:
Release Date : 1985
Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators written by Maksim M. Skriganov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Multidimensional Periodic Schr Dinger Operator
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Author : Oktay Veliev
language : en
Publisher: Springer Nature
Release Date : 2024-02-27
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 2024-02-27 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 and significantly expanded third edition features an extension of this framework to all dimensions, offering a now complete theory of self-adjoint Schrödinger operators within periodic potentials. Drawing from recent advancements in mathematical analysis, this edition delves even deeper into the intricacies of the subject. It explores the connections between the multidimensional Schrödinger operator, periodic potentials, and other fundamental areas of mathematical physics. The book's comprehensive approach equips both students and researchers with the tools to tackle complex problems and contribute to the ongoing exploration of quantum phenomena.
Analysis And Geometry On Graphs And Manifolds
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Author : Matthias Keller
language : en
Publisher: Cambridge University Press
Release Date : 2020-08-20
Analysis And Geometry On Graphs And Manifolds written by Matthias Keller and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-20 with Mathematics categories.
A contemporary exploration of the interplay between geometry, spectral theory and stochastics which is explored for graphs and manifolds.
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.
Integral Methods In Science And Engineering
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Author : Christian Constanda
language : en
Publisher: Springer Nature
Release Date : 2022-10-13
Integral Methods In Science And Engineering written by Christian Constanda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-13 with Mathematics categories.
This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Symposium on the Theory and Applications of Integral Methods in Science and Engineering, held virtually in July 2021, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.
Mathematical Modeling In Optical Science
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Author : Gang Bao
language : en
Publisher: SIAM
Release Date : 2001-01-01
Mathematical Modeling In Optical Science written by Gang Bao and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Science categories.
This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.
Waves In Periodic And Random Media
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Author : Peter Kuchment
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Waves In Periodic And Random Media written by Peter Kuchment and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Science and engineering have been great sources of problems and inspiration for generations of mathematicians. This is probably true now more than ever as numerous challenges in science and technology are met by mathematicians. One of these challenges is understanding propagation of waves of different nature in systems of complex structure. This book contains the proceedings of the research conference, ``Waves in Periodic and Random Media''. Papers are devoted to a number of related themes, including spectral theory of periodic differential operators, Anderson localization and spectral theory of random operators, photonic crystals, waveguide theory, mesoscopic systems, and designer random surfaces. Contributions are written by prominent experts and are of interest to researchers and graduate students in mathematical physics.
Introduction To Quantum Graphs
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Author : Gregory Berkolaiko
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Introduction To Quantum Graphs written by Gregory Berkolaiko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.
Solvable Models In Quantum Mechanics
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Author : Sergio Albeverio
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Solvable Models In Quantum Mechanics written by Sergio Albeverio and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
"This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided. The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988."--Résumé de l'éditeur.