Perturbation Theory For The Schrodinger Operator With A Periodic Potential

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Perturbation Theory for the Schrödinger Operator with a Periodic Potential

Author : Yulia E. Karpeshina
Publisher : Springer
ISBN 13 : 3540691561
Total Pages : 358 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Perturbation Theory for the Schrödinger Operator with a Periodic Potential by : Yulia E. Karpeshina

Download or read book Perturbation Theory for the Schrödinger Operator with a Periodic Potential written by Yulia E. Karpeshina and published by Springer. This book was released on 2006-11-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Yulia E. Karpeshina
Publisher :
ISBN 13 : 9783662212660
Total Pages : 364 pages
Book Rating : 4.2/5 (126 download)

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Book Synopsis Perturbation Theory for the Schrodinger Operator with a Periodic Potential by : Yulia E. Karpeshina

Download or read book Perturbation Theory for the Schrodinger Operator with a Periodic Potential written by Yulia E. Karpeshina and published by . This book was released on 2014-01-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multidimensional Periodic Schrödinger Operator

Author : Oktay Veliev
Publisher : Springer
ISBN 13 : 3319166433
Total Pages : 249 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Multidimensional Periodic Schrödinger Operator by : Oktay Veliev

Download or read book Multidimensional Periodic Schrödinger Operator written by Oktay Veliev and published by Springer. This book was released on 2015-03-28 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday

Author : Fritz Gesztesy
Publisher : American Mathematical Soc.
ISBN 13 : 082184248X
Total Pages : 528 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday by : Fritz Gesztesy

Download or read book Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday written by Fritz Gesztesy and published by American Mathematical Soc.. This book was released on 2007 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to aparticular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random andErgodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensiveintroduction into an area covered in this volume.

Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two

Author : Yulia Karpeshina
Publisher : American Mathematical Soc.
ISBN 13 : 1470435438
Total Pages : 152 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two by : Yulia Karpeshina

Download or read book Extended States for the Schrödinger Operator with Quasi-Periodic Potential in Dimension Two written by Yulia Karpeshina and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a Schrödinger operator H=−Δ+V(x⃗ ) in dimension two with a quasi-periodic potential V(x⃗ ). They prove that the absolutely continuous spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves ei⟨ϰ⃗ ,x⃗ ⟩ in the high energy region. Second, the isoenergetic curves in the space of momenta ϰ⃗ corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results. The result is based on a previous paper on the quasiperiodic polyharmonic operator (−Δ)l+V(x⃗ ), l>1. Here the authors address technical complications arising in the case l=1. However, this text is self-contained and can be read without familiarity with the previous paper.

Non-self-adjoint Schrödinger Operator with a Periodic Potential

Author : Oktay Veliev
Publisher : Springer Nature
ISBN 13 : 3030726835
Total Pages : 301 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Non-self-adjoint Schrödinger Operator with a Periodic Potential by : Oktay Veliev

Download or read book Non-self-adjoint Schrödinger Operator with a Periodic Potential written by Oktay Veliev and published by Springer Nature. This book was released on 2021-06-19 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete spectral analysis of the non-self-adjoint Schrödinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schrödinger operator, the book features a complete spectral analysis of the Mathieu-Schrödinger operator and the Schrödinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.

Mathematical Modeling in Optical Science

Author : Gang Bao
Publisher : SIAM
ISBN 13 : 0898714753
Total Pages : 344 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Mathematical Modeling in Optical Science by : Gang Bao

Download or read book Mathematical Modeling in Optical Science written by Gang Bao and published by SIAM. This book was released on 2001-01-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. Chapters present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. Although some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields.

Schrödinger Operators

Author : Hans L. Cycon
Publisher : Springer Science & Business Media
ISBN 13 : 3540167587
Total Pages : 337 pages
Book Rating : 4.5/5 (41 download)

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Book Synopsis Schrödinger Operators by : Hans L. Cycon

Download or read book Schrödinger Operators written by Hans L. Cycon and published by Springer Science & Business Media. This book was released on 1987 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Floquet Theory for Partial Differential Equations

Author : P.A. Kuchment
Publisher : Birkhäuser
ISBN 13 : 3034885733
Total Pages : 363 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Floquet Theory for Partial Differential Equations by : P.A. Kuchment

Download or read book Floquet Theory for Partial Differential Equations written by P.A. Kuchment and published by Birkhäuser. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].

Methods of Spectral Analysis in Mathematical Physics

Author : Jan Janas
Publisher : Springer Science & Business Media
ISBN 13 : 3764387556
Total Pages : 437 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Methods of Spectral Analysis in Mathematical Physics by : Jan Janas

Download or read book Methods of Spectral Analysis in Mathematical Physics written by Jan Janas and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.

Boundary Value Problems of Mathematical Physics

Author : Olʹga A. Ladyženskaja
Publisher : American Mathematical Soc.
ISBN 13 : 9780821831410
Total Pages : 254 pages
Book Rating : 4.8/5 (314 download)

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Book Synopsis Boundary Value Problems of Mathematical Physics by : Olʹga A. Ladyženskaja

Download or read book Boundary Value Problems of Mathematical Physics written by Olʹga A. Ladyženskaja and published by American Mathematical Soc.. This book was released on 1991 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Perturbation Theory in Periodic Problems for Two-Dimensional Integrable Systems

Author : I. M. Krichever
Publisher : CRC Press
ISBN 13 : 9783718652181
Total Pages : 118 pages
Book Rating : 4.6/5 (521 download)

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Book Synopsis Perturbation Theory in Periodic Problems for Two-Dimensional Integrable Systems by : I. M. Krichever

Download or read book Perturbation Theory in Periodic Problems for Two-Dimensional Integrable Systems written by I. M. Krichever and published by CRC Press. This book was released on 1992 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Waves in Periodic and Random Media

Author : Peter Kuchment
Publisher : American Mathematical Soc.
ISBN 13 : 0821832867
Total Pages : 232 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Waves in Periodic and Random Media by : Peter Kuchment

Download or read book Waves in Periodic and Random Media written by Peter Kuchment and published by American Mathematical Soc.. This book was released on 2003 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Microlocal Analysis, Sharp Spectral Asymptotics and Applications V

Author : Victor Ivrii
Publisher : Springer Nature
ISBN 13 : 3030305619
Total Pages : 761 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Microlocal Analysis, Sharp Spectral Asymptotics and Applications V by : Victor Ivrii

Download or read book Microlocal Analysis, Sharp Spectral Asymptotics and Applications V written by Victor Ivrii and published by Springer Nature. This book was released on 2019-09-13 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I, II, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.

Geometric and Arithmetic Methods in the Spectral Theory of Multidimensional Periodic Operators

Author : M. M. Skriganov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821831045
Total Pages : 132 pages
Book Rating : 4.8/5 (31 download)

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Book Synopsis Geometric and Arithmetic Methods in the Spectral Theory of Multidimensional Periodic Operators by : M. M. Skriganov

Download or read book Geometric and Arithmetic Methods in the Spectral Theory of Multidimensional Periodic Operators written by M. M. Skriganov and published by American Mathematical Soc.. This book was released on 1987 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Operator Theory

Author : Aref Jeribi
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110598191
Total Pages : 228 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Operator Theory by : Aref Jeribi

Download or read book Operator Theory written by Aref Jeribi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-03-22 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume collects select contributions presented at the International Conference in Operator Theory held at Hammamet, Tunisia, on April 30 May 3, 2018. Edited and refereed by well-known experts in the field, this wide-ranging collection of survey and research articles presents the state of the art in the field of operator theory, covering topics such as operator and spectral theory, fixed point theory, functional analysis etc.

Partial Differential Equations and Inverse Problems

Author : Carlos Conca
Publisher : American Mathematical Soc.
ISBN 13 : 0821834487
Total Pages : 426 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Partial Differential Equations and Inverse Problems by : Carlos Conca

Download or read book Partial Differential Equations and Inverse Problems written by Carlos Conca and published by American Mathematical Soc.. This book was released on 2004 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is a collection of articles from the Pan-American Advanced Studies Institute on partial differential equations, nonlinear analysis and inverse problems held in Santiago (Chile). Interactions among partial differential equations, nonlinear analysis, and inverse problems have produced remarkable developments over the last couple of decades. This volume contains survey articles reflecting the work of leading experts who presented minicourses at the event. Contributors include J. Busca, Y. Capdeboscq, M.S. Vogelius, F. A. Grunbaum, L. F. Matusevich, M. de Hoop, and P. Kuchment. The volume is suitable for graduate students and researchers interested in partial differential equations and their applications in nonlinear analysis and inverse problems.