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Operator Theoretical Methods And Applications To Mathematical Physics
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Book Synopsis Operator Theoretical Methods and Applications to Mathematical Physics by : Israel Gohberg
Download or read book Operator Theoretical Methods and Applications to Mathematical Physics written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the life and work of the applied mathematician Professor Erhard Meister (1930-2001). He was a member of the editorial boards of this book series Operator The ory: Advances and Applications as well as of the journal Integral Equations and Operator Theory, both published by Birkhauser (now part of Springer-Verlag). Moreover he played a decisive role in the foundation of these two series by helping to establish contacts between Birkhauser and the founder and present chief editor of this book series after his emigration from Moldavia in 1974. The volume is divided into two parts. Part A contains reminiscences about the life of E. Meister including a short biography and an exposition of his professional work. Part B displays the wide range of his scientific interests through eighteen original papers contributed by authors with close scientific and personal relations to E. Meister. We hope that a great part of the numerous features of his life and work can be re-discovered from this book.
Book Synopsis Operator Theory, Analysis and Mathematical Physics by : Jan Janas
Download or read book Operator Theory, Analysis and Mathematical Physics written by Jan Janas and published by Springer Science & Business Media. This book was released on 2007-04-29 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures delivered at the International Conference Operator Theory and its Applications in Mathematical Physics (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics.
Book Synopsis Mathematical Methods in Physics by : Philippe Blanchard
Download or read book Mathematical Methods in Physics written by Philippe Blanchard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.
Book Synopsis Operator Theoretical Methods and Applications to Mathematical Physics by : Erhard Meister
Download or read book Operator Theoretical Methods and Applications to Mathematical Physics written by Erhard Meister and published by Birkhauser. This book was released on 2004-01-01 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operators, Geometry and Quanta by : Dmitri Fursaev
Download or read book Operators, Geometry and Quanta written by Dmitri Fursaev and published by Springer Science & Business Media. This book was released on 2011-06-25 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.
Book Synopsis Mathematical Methods in Quantum Mechanics by : Gerald Teschl
Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2009 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).
Book Synopsis Operator Methods in Mathematical Physics by : Jan Janas
Download or read book Operator Methods in Mathematical Physics written by Jan Janas and published by Springer Science & Business Media. This book was released on 2013-01-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference Operator Theory, Analysis and Mathematical Physics – OTAMP is a regular biennial event devoted to mathematical problems on the border between analysis and mathematical physics. The current volume presents articles written by participants, mostly invited speakers, and is devoted to problems at the forefront of modern mathematical physics such as spectral properties of CMV matrices and inverse problems for the non-classical Schrödinger equation. Other contributions deal with equations from mathematical physics and study their properties using methods of spectral analysis. The volume explores several new directions of research and may serve as a source of new ideas and problems for all scientists interested in modern mathematical physics.
Book Synopsis Topics in Operator Theory by : Joseph A. Ball
Download or read book Topics in Operator Theory written by Joseph A. Ball and published by Springer Science & Business Media. This book was released on 2011-02-03 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.
Book Synopsis Mathematical Methods in Physics by : Philippe Blanchard
Download or read book Mathematical Methods in Physics written by Philippe Blanchard and published by Birkhäuser. This book was released on 2015-04-07 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three parts: - Part I: A brief introduction to (Schwartz) distribution theory. Elements from the theories of ultra distributions and (Fourier) hyperfunctions are given in addition to some deeper results for Schwartz distributions, thus providing a rather comprehensive introduction to the theory of generalized functions. Basic properties and methods for distributions are developed with applications to constant coefficient ODEs and PDEs. The relation between distributions and holomorphic functions is considered, as well as basic properties of Sobolev spaces. - Part II: Fundamental facts about Hilbert spaces. The basic theory of linear (bounded and unbounded) operators in Hilbert spaces and special classes of linear operators - compact, Hilbert-Schmidt, trace class, and Schrödinger operators, as needed in quantum physics and quantum information theory – are explored. This section also contains a detailed spectral analysis of all major classes of linear operators, including completeness of generalized eigenfunctions, as well as of (completely) positive mappings, in particular quantum operations. - Part III: Direct methods of the calculus of variations and their applications to boundary- and eigenvalue-problems for linear and nonlinear partial differential operators. The authors conclude with a discussion of the Hohenberg-Kohn variational principle. The appendices contain proofs of more general and deeper results, including completions, basic facts about metrizable Hausdorff locally convex topological vector spaces, Baire’s fundamental results and their main consequences, and bilinear functionals. Mathematical Methods in Physics is aimed at a broad community of graduate students in mathematics, mathematical physics, quantum information theory, physics and engineering, as well as researchers in these disciplines. Expanded content and relevant updates will make this new edition a valuable resource for those working in these disciplines.
Book Synopsis Non-Selfadjoint Operators in Quantum Physics by : Fabio Bagarello
Download or read book Non-Selfadjoint Operators in Quantum Physics written by Fabio Bagarello and published by John Wiley & Sons. This book was released on 2015-07-24 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.
Book Synopsis Spectral Methods for Operators of Mathematical Physics by : Jan Janas
Download or read book Spectral Methods for Operators of Mathematical Physics written by Jan Janas and published by Birkhäuser. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent results in the following areas: spectral analysis of one-dimensional Schrödinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. Several developments treated appear for the first time in a book. It is addressed to a wide group of specialists working in operator theory or mathematical physics.
Book Synopsis Operator Theory, Analysis and Mathematical Physics by : Jan Janas
Download or read book Operator Theory, Analysis and Mathematical Physics written by Jan Janas and published by Birkhäuser. This book was released on 2009-09-03 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures delivered at the International Conference Operator Theory and its Applications in Mathematical Physics (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics.
Book Synopsis Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics by : Wolfgang Arendt
Download or read book Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics written by Wolfgang Arendt and published by Birkhäuser. This book was released on 2015-12-10 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event. They will be a valuable and inspiring source of information for graduate students and established researchers.
Book Synopsis Schrödinger Operators by : Hans L. Cycon
Download or read book Schrödinger Operators written by Hans L. Cycon and published by Springer. This book was released on 2009-08-19 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operator Methods in Quantum Mechanics by : Martin Schechter
Download or read book Operator Methods in Quantum Mechanics written by Martin Schechter and published by Courier Corporation. This book was released on 2014-06-10 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces techniques related to physical theory. Entire book is devoted to a particle moving in a straight line; students develop techniques by answering questions about the particle. 1981 edition.
Book Synopsis Algebraic Methods in Operator Theory by : Raúl E. Curto
Download or read book Algebraic Methods in Operator Theory written by Raúl E. Curto and published by . This book was released on 1994-01-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operator Algebras and Mathematical Physics by : Tirthankar Bhattacharyya
Download or read book Operator Algebras and Mathematical Physics written by Tirthankar Bhattacharyya and published by Birkhäuser. This book was released on 2015-09-29 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers contributions from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Bangalore, India, in December 2013. All articles were written by experts and cover a broad range of original material at the cutting edge of operator theory and its applications. Topics include multivariable operator theory, operator theory on indefinite metric spaces (Krein and Pontryagin spaces) and its applications, spectral theory with applications to differential operators, the geometry of Banach spaces, scattering and time varying linear systems, and wavelets and coherent states.
