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Author : Pavel Exner
Publisher :
ISBN 13 : 9783662137611
Total Pages : 288 pages
Book Rating : 4.1/5 (376 download)
Download or read book Applications of Self-Adjoint Extensions in Quantum Physics written by Pavel Exner and published by . This book was released on 2014-01-15 with total page 288 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.
Download or read book Applications of self-adjoint extensions in quantum physics written by and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Matteo Gallone
Publisher : Springer Nature
ISBN 13 : 303110885X
Total Pages : 557 pages
Book Rating : 4.0/5 (311 download)
Download or read book Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians written by Matteo Gallone and published by Springer Nature. This book was released on 2023-04-04 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac–Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.
Author : Fabio Bagarello
Publisher : John Wiley & Sons
ISBN 13 : 1118855264
Total Pages : 434 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 2015-07-24 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.
Author : Jirí Blank
Publisher : Springer Science & Business Media
ISBN 13 : 1402088701
Total Pages : 677 pages
Book Rating : 4.4/5 (2 download)
Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank and published by Springer Science & Business Media. This book was released on 2008-09-24 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.
Author : Springer
Publisher :
ISBN 13 : 9780817671884
Total Pages : 528 pages
Book Rating : 4.6/5 (718 download)
Download or read book Self-Adjoint Extensions in Quantum Mechanics written by Springer and published by . This book was released on 2012-04-28 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Scott J. Beck
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (971 download)
Download or read book Application of Self-adjoint Extensions to the Relativistic and Non-relativistic Coulomb Problem written by Scott J. Beck and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Coulomb problem was one of the first successful applications of quantum theory and is a staple topic in textbooks. However there is an ambiguity in the solution to the problem that is seldom discussed in either textbooks or the literature. The ambiguity arises in the boundary conditions that must be applied at the origin where the Coulomb potential is singular. The textbook boundary condition is generally not the only one that is permissible or the one that is most appropriate. Here we revisit the question of boundary conditions using the mathematical method of self-adjoint extensions in context of modern realizations of the Coulomb problem in electrons on helium, Rydberg atoms and graphene. We determine the family of allowed boundary conditions for the non-relativistic Schr\"{o}dinger equation in one and three dimensions and the relativistic Dirac equation in two dimensions. The boundary conditions are found to break the classical SO$(4)$ Runge-Lenz symmetry of the non-relativistic Coulomb problem in three dimensions and to break scale invariance for the two dimensional Dirac problem. The symmetry breaking is analogous to the anomaly phenomenon in quantum field theory. Electrons on helium have been extensively studied for their potential use in quantum computing and as a laboratory for condensed matter physics. The trapped electrons provide a realization of the one dimensional non-relativistic Coulomb problem. Using the method of self-adjoint extensions we are able to reproduce the observed energy levels of electrons on helium which are known to deviate from the textbook Balmer formula. We also study the connection between the method of self-adjoint extensions and an older theoretical model introduced by Cole. Rydberg atoms have potential applications to atomic clocks and precision atomic experiments. They are hydrogen-like in that they have a single highly excited electron that orbits a small positively charged core. We compare the observed spectrum of several species of Rydberg atoms to the predictions of the Coulomb model with self-adjoint extension and to the predictions of the more elaborate quantum defect model which is generally found to be more accurate. The motion of electrons on atomically flat sheets of graphene is governed by the massless Dirac equation. The effect of charged impurities on the electronic states of graphene has been studied using scanning probe microscopy. Here we use the method of self-adjoint extensions to analyze the scattering of electrons from the charged impurities; our results generalize prior theoretical work which considered only one of the family of possible boundary conditions.
Author : Darren J. Platt
Publisher :
ISBN 13 :
Total Pages : 85 pages
Book Rating : 4.:/5 (268 download)
Download or read book Self-adjoint extensions and quantum mechanics written by Darren J. Platt and published by . This book was released on 2005 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Horst R. Beyer
Publisher : Springer Nature
ISBN 13 : 3031490789
Total Pages : 222 pages
Book Rating : 4.0/5 (314 download)
Download or read book Introduction to Quantum Mechanics written by Horst R. Beyer and published by Springer Nature. This book was released on with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Konstantin A Makarov
Publisher : World Scientific
ISBN 13 : 9811241244
Total Pages : 300 pages
Book Rating : 4.8/5 (112 download)
Download or read book Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements written by Konstantin A Makarov and published by World Scientific. This book was released on 2021-12-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory.In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jørgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs.The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated 'double-slit experiment' where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring.
Author : Michael Reed
Publisher : Elsevier
ISBN 13 : 0080925375
Total Pages : 380 pages
Book Rating : 4.0/5 (89 download)
Download or read book II: Fourier Analysis, Self-Adjointness written by Michael Reed and published by Elsevier. This book was released on 1975-11-05 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.
Author : César R. de Oliveira
Publisher : Springer Science & Business Media
ISBN 13 : 3764387955
Total Pages : 418 pages
Book Rating : 4.7/5 (643 download)
Download or read book Intermediate Spectral Theory and Quantum Dynamics written by César R. de Oliveira and published by Springer Science & Business Media. This book was released on 2008-12-30 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics. Many examples and exercises are included that focus on quantum mechanics.
Author : Gerald Teschl
Publisher : American Mathematical Soc.
ISBN 13 : 0821846604
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)
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).
Author : Michael Reed
Publisher : Elsevier
ISBN 13 : 9780125850025
Total Pages : 388 pages
Book Rating : 4.8/5 (5 download)
Download or read book II: Fourier Analysis, Self-Adjointness written by Michael Reed and published by Elsevier. This book was released on 1975 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Band 2.
Author : Manuel Gadella
Publisher : Frontiers Media SA
ISBN 13 : 2889665925
Total Pages : 182 pages
Book Rating : 4.8/5 (896 download)
Download or read book Contact Interactions in Quantum Mechanics: Theory, Mathematical Aspects and Applications written by Manuel Gadella and published by Frontiers Media SA. This book was released on 2021-03-12 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Asim Orhan Barut
Publisher : World Scientific
ISBN 13 : 9789971502171
Total Pages : 750 pages
Book Rating : 4.5/5 (21 download)
Download or read book Theory of Group Representations and Applications written by Asim Orhan Barut and published by World Scientific. This book was released on 1986 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
