Download or read book Quantum Mechanics in Phase Space written by Cosmas Zachos and published by World Scientific. This book was released on 2005 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wigner's quasi-probability distribution function in phase space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence, quantum computing, and quantum chaos. It is also important in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative, formulation of quantum mechanics, independent of the conventional Hilbert space, or path integral formulations.In this logically complete and self-standing formulation, one need not choose sides ? coordinate or momentum space. It works in full phase space, accommodating the uncertainty principle, and it offers unique insights into the classical limit of quantum theory. This invaluable book is a collection of the seminal papers on the formulation, with an introductory overview which provides a trail map for those papers; an extensive bibliography; and simple illustrations, suitable for applications to a broad range of physics problems. It can provide supplementary material for a beginning graduate course in quantum mechanics.

Download or read book Phase Space Picture Of Quantum Mechanics Group Theoretical Approach written by Young Suh Kim and published by World Scientific. This book was released on 1991-03-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.

Download or read book Quantum Optics in Phase Space written by Wolfgang P. Schleich and published by John Wiley & Sons. This book was released on 2015-12-11 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

Download or read book Quantum Mechanics on Phase Space written by Franklin E. Schroeck Jr. and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967].

Download or read book A Concise Treatise on Quantum Mechanics in Phase Space written by Thomas Curtright and published by World Scientific Publishing Company Incorporated. This book was released on 2014 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions density matrices in a special Weyl representation and star products are the cornerstones of the formalism. The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. In this logically complete and self-standing formulation, one need not choose sides between coordinate or momentum space variables. It works in full phase-space, accommodating the uncertainty principle; and it offers unique insights into the classical limit of quantum theory. The observables in this formulation are c-number functions in phase space instead of operators, with the same interpretation as their classical counterparts, only composed together in novel algebraic ways using star products. This treatise provides an introductory overview and supplementary material suitable for an advanced undergraduate or a beginning graduate course in quantum mechanics.

Download or read book The Physics of Phase Space written by Young S. Kim and published by Springer. This book was released on 2005-09-13 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study of the Wigner distribution. This volume gives the first complete survey of the progress made by both mathematicians and physicists. It will serve as an excellent reference for further research.

Download or read book Symplectic Geometry and Quantum Mechanics written by Maurice A. de Gosson and published by Springer Science & Business Media. This book was released on 2006-08-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.

Download or read book A Concise Treatise On Quantum Mechanics In Phase Space written by Thomas L Curtright and published by World Scientific Publishing Company. This book was released on 2013-11-11 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions — density matrices in a special Weyl representation — and star products are the cornerstones of the formalism.The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject.In this logically complete and self-standing formulation, one need not choose sides between coordinate or momentum space variables. It works in full phase space, accommodating the uncertainty principle; and it offers unique insights into the classical limit of quantum theory. The observables in this formulation are c-number functions in phase space instead of operators, with the same interpretation as their classical counterparts, only composed together in novel algebraic ways using star products.This treatise provides an introductory overview and supplementary material suitable for an advanced undergraduate or a beginning graduate course in quantum mechanics.

Download or read book Advanced Topics in Quantum Mechanics written by Marcos Mariño and published by Cambridge University Press. This book was released on 2021-12-09 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout.

Download or read book Quantum Analogues From Phase Transitions to Black Holes and Cosmology written by William Unruh and published by Springer. This book was released on 2007-04-14 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, analogies between laboratory physics (e.g. quantum optics and condensed matter) and gravitational/cosmological phenomena such as black holes have attracted an increasing interest. This book contains a series of selected lectures devoted to this new and rapidly developing field. Various analogies connecting (apparently) different areas in physics are presented in order to bridge the gap between them and to provide an alternative point of view.

Download or read book Principles of Quantum Mechanics written by R. Shankar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

Download or read book Linear Ray and Wave Optics in Phase Space written by Amalia Torre and published by Elsevier. This book was released on 2020-06-01 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Ray and Wave Optics in Phase Space, Second Edition, is a comprehensive introduction to Wigner optics. The book connects ray and wave optics, offering the optical phase space as the ambience and the Wigner function based technique as the mathematical machinery to accommodate between the two opposite extremes of light representation: the localized ray of geometrical optics and the unlocalized wave function of wave optics. Analogies with other branches of classical and quantum physics—such as classical and quantum mechanics, quantum optics, signal theory and magnetic optics—are evidenced by pertinent comments and/or rigorous mathematics. Lie algebra and group methods are introduced and explained through the elementary optical systems within the ray and wave optics contexts, the former being related to the symplectic group and the latter to the metaplectic group. In a similar manner, the Wigner function is introduced by following the original issue to individualize a phase space representation of quantum mechanics, which is mirrored by the issue to individualize a local frequency spectrum within the signal theory context. The basic analogy with the optics of charged particles inherently underlying the ray-optics picture in phase space is also evidenced within the wave-optics picture in the Wigner phase space. This second edition contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics. All chapters are fully revised and updated. All topics have been developed to a deeper level than in the previous edition and are now supported with Mathematica and Mathcad codes. Provides powerful tools to solve problems in quantum mechanics, quantum optics and signal theory Includes numerous examples supporting a gradual and comprehensive introduction to Wigner optics Treats both ray and wave optics, resorting to Lie-algebra based methods Connects the subject with other fields, such as quantum optics, quantum mechanics, signal theory and optics of charged particles Introduces abstract concepts through concrete examples Includes logical diagrams to introduce mathematics in an intuitive way Contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics Supported with Mathematica and Mathcad codes

Download or read book Quantum Dynamics with Trajectories written by Robert E. Wyatt and published by Springer Science & Business Media. This book was released on 2006-05-28 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a rapidly developing field to which the author is a leading contributor New methods in quantum dynamics and computational techniques, with applications to interesting physical problems, are brought together in this book Useful to both students and researchers

Download or read book Geometric Phases in Classical and Quantum Mechanics written by Dariusz Chruscinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.

Download or read book Principles Of Newtonian And Quantum Mechanics The The Need For Planck s Constant H Second Edition written by Maurice A De Gosson and published by World Scientific. This book was released on 2016-11-10 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book deals, as the first, with the foundations of classical physics from the 'symplectic' point of view, and of quantum mechanics from the 'metaplectic' point of view. We have revised and augmented the topics studied in the first edition in the light of new results, and added several new sections. The Bohmian interpretation of quantum mechanics is discussed in detail. Phase space quantization is achieved using the 'principle of the symplectic camel', which is a deep topological property of Hamiltonian flows. We introduce the notion of 'quantum blob', which can be viewed as the fundamental phase space unit. The mathematical tools developed in this book are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the 'metatron' is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.

Download or read book Harmonic Analysis in Phase Space written by G. B. Folland and published by Princeton University Press. This book was released on 1989-03-21 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

Download or read book From Classical to Quantum Mechanics written by Giampiero Esposito and published by Cambridge University Press. This book was released on 2004-03-11 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.