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Author : Cecil Eldon Leith
Publisher :
ISBN 13 :
Total Pages : 252 pages
Book Rating : 4.:/5 (29 download)
Download or read book One-dimensional Perturbation of Unbound Self-adjoint Operators written by Cecil Eldon Leith and published by . This book was released on 1957 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D.M. Gitman
Publisher : Springer Science & Business Media
ISBN 13 : 0817646620
Total Pages : 523 pages
Book Rating : 4.8/5 (176 download)
Download or read book Self-adjoint Extensions in Quantum Mechanics written by D.M. Gitman and published by Springer Science & Business Media. This book was released on 2012-04-27 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert spaces. The authors begin by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes to the naive treatment. It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems. In the end, related problems in quantum field theory are briefly introduced. This well-organized text is most suitable for students and post graduates interested in deepening their understanding of mathematical problems in quantum mechanics. However, scientists in mathematical and theoretical physics and mathematicians will also find it useful.
Author : Konrad Schmüdgen
Publisher : Springer Science & Business Media
ISBN 13 : 9400747535
Total Pages : 435 pages
Book Rating : 4.4/5 (7 download)
Download or read book Unbounded Self-adjoint Operators on Hilbert Space written by Konrad Schmüdgen and published by Springer Science & Business Media. This book was released on 2012-07-09 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension
Author : W.G. Faris
Publisher : Springer
ISBN 13 : 3540373179
Total Pages : 123 pages
Book Rating : 4.5/5 (43 download)
Download or read book Self-Adjoint Operators written by W.G. Faris and published by Springer. This book was released on 2006-11-15 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Johannes Sjöstrand
Publisher : Springer
ISBN 13 : 3030108198
Total Pages : 496 pages
Book Rating : 4.0/5 (31 download)
Download or read book Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations written by Johannes Sjöstrand and published by Springer. This book was released on 2019-05-17 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Author : John R. Ringrose
Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.:/5 (44 download)
Download or read book Compact Non-self-adjoint Operators written by John R. Ringrose and published by . This book was released on 1971 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Volodymyr Koshmanenko
Publisher : Birkhäuser
ISBN 13 : 3319295357
Total Pages : 237 pages
Book Rating : 4.3/5 (192 download)
Download or read book The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators written by Volodymyr Koshmanenko and published by Birkhäuser. This book was released on 2016-07-08 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadratic forms, and the theory of rigged Hilbert spaces. The book will appeal to researchers in mathematics and mathematical physics studying the scales of densely embedded Hilbert spaces, the singular perturbations phenomenon, and singular interaction problems.
Author : Aref Jeribi
Publisher : Springer Nature
ISBN 13 : 981162528X
Total Pages : 509 pages
Book Rating : 4.8/5 (116 download)
Download or read book Perturbation Theory for Linear Operators written by Aref Jeribi and published by Springer Nature. This book was released on 2021-07-28 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.
Author : Ann Arnquist Mills
Publisher :
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.3/5 (121 download)
Download or read book Perturbation Effects on Fine Spectral Structure of Operations written by Ann Arnquist Mills and published by . This book was released on 1976 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fabio Bagarello
Publisher : John Wiley & Sons
ISBN 13 : 1118855280
Total Pages : 433 pages
Book Rating : 4.1/5 (188 download)
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 2015-07-20 with total page 433 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.
Author : John Locker
Publisher : American Mathematical Soc.
ISBN 13 : 0821820494
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)
Download or read book Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators written by John Locker and published by American Mathematical Soc.. This book was released on 2000 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the spectral theory of an nth order non-self-adjoint two- point differential operator L in the complex Hilbert space L2[0,1]. The differential operator L is determined by an nth order formal differential l and by n linearly independent boundary values B1,.,Bn. Locker first lays the foundations of the spectral theory for closed linear operators and Fredholm operators in Hilbert spaces before developing the spectral theory of the differential operator L. The book is a sequel to Functional analysis and two-point differential operators, 1986. Annotation copyrighted by Book News, Inc., Portland, OR.
Author : Tosio Katō
Publisher : Springer
ISBN 13 :
Total Pages : 652 pages
Book Rating : 4.3/5 (91 download)
Download or read book Perturbation Theory for Linear Operators written by Tosio Katō and published by Springer. This book was released on 1976 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michel Janssen
Publisher : Oxford University Press
ISBN 13 : 0198883919
Total Pages : 817 pages
Book Rating : 4.1/5 (988 download)
Download or read book Constructing Quantum Mechanics Volume 2 written by Michel Janssen and published by Oxford University Press. This book was released on 2023-08-15 with total page 817 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes on the genesis of quantum mechanics in the first quarter of the 20th century. It covers the period 1923-1927. After covering some of the difficulties the old quantum theory had run into by the early 1920s as well as the discovery of the exclusion principle and electron spin, it traces the emergence of two forms of the new quantum mechanics, matrix mechanics and wave mechanics, in the years 1923-27. It then shows how the new theory took care of some of the failures of the old theory and put its successes on a more solid basis. Finally, it shows how in 1927 the two forms of the new theory were unified, first through statistical transformation theory, then through the Hilbert space formalism. This volume provides a detailed analysis of the classic papers by Heisenberg, Born, Jordan, Dirac, De Broglie, Einstein, Schrödinger, von Neumann and other authors. Drawing on the correspondence of these and other physicists, their later reminiscences and the extensive secondary literature on the “quantum revolution”, this volume places these papers in the context of the discussions out of which modern quantum mechanics emerged. It argues that the genesis of modern quantum mechanics can be seen as the construction of an arch on a scaffold provided by the old quantum theory, discarded once the arch could support itself.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John Roe
Publisher : Longman Scientific and Technical
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.3/5 (91 download)
Download or read book Elliptic Operators, Topology, and Asymptotic Methods written by John Roe and published by Longman Scientific and Technical. This book was released on 1988 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Stone
Publisher : Cambridge University Press
ISBN 13 : 1139480618
Total Pages : 821 pages
Book Rating : 4.1/5 (394 download)
Download or read book Mathematics for Physics written by Michael Stone and published by Cambridge University Press. This book was released on 2009-07-09 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
Author :
Publisher :
ISBN 13 :
Total Pages : 914 pages
Book Rating : 4.3/5 (91 download)
Download or read book Physics Briefs written by and published by . This book was released on 1986 with total page 914 pages. Available in PDF, EPUB and Kindle. Book excerpt:
