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Phase Space Picture Of Quantum Mechanics Group Theoretical Approach
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Book Synopsis Phase Space Picture of Quantum Mechanics by : Y. S. Kim
Download or read book Phase Space Picture of Quantum Mechanics written by Y. S. Kim and published by World Scientific. This book was released on 1991 with total page 356 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 Schrdinger 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.
Author :Franklin E. Schroeck Jr. Publisher :Springer Science & Business Media ISBN 13 :9401728305 Total Pages :687 pages Book Rating :4.4/5 (17 download)
Book Synopsis Quantum Mechanics on Phase Space by : Franklin E. Schroeck Jr.
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].
Book Synopsis Phase Space Picture Of Quantum Mechanics: Group Theoretical Approach by : Young Suh Kim
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.
Book Synopsis Quantum Mechanics in Phase Space by : Cosmas Zachos
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.
Book Synopsis A Concise Treatise On Quantum Mechanics In Phase Space by : Thomas L Curtright
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.
Book Synopsis Group Theoretical Methods in Physics by : M. A. Markov
Download or read book Group Theoretical Methods in Physics written by M. A. Markov and published by CRC Press. This book was released on 1985 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis From Micro to Macro Quantum Systems by : K. Kong Wan
Download or read book From Micro to Macro Quantum Systems written by K. Kong Wan and published by World Scientific. This book was released on 2006 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations.This book also discusses various topics of interest such as the asymptotic treatment of quantum state preparation and quantum measurement, local observables and local values, Schrdinger's cat states in superconducting systems, and a path space formulation of quantum mechanics.This self-contained book is complete with a review of relevant geometric and operator theories, for example, vector fields and operators, symmetric operators and their maximal symmetric extensions, direct integrals of Hilbert spaces and operators.
Book Synopsis Symplectic Quantum Field Theory by : Ademir E. Santana
Download or read book Symplectic Quantum Field Theory written by Ademir E. Santana and published by Cambridge Scholars Publishing. This book was released on 2023-12-21 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph brings to readers, as researchers and students of physics and mathematics, recent developments in symmetries, where the representation space is a symplectic manifold. This gives rise to the quantum field theory formulated in through the concept of phase space and associated with the Wigner function, a quasi-distribution of probability. This approach provides information about non-classicality of quantum systems, describes quantum chaos and is the starting point of the quantum kinetic theory. In this realm, abelian and non-abelian gauge symmetries are introduced with the concept of quasi-amplitude of probability. This leads, for instance, to Symplectic Schrödinger, Klein-Gordon and Dirac equations dealing with systems in condensed matter and particle physics. These achievements are depicted here, following a pedagogical model of presentation.
Book Synopsis A Concise Treatise on Quantum Mechanics in Phase Space by : Thomas Curtright
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.
Author :Maria Luisa Dalla Chiara Publisher :Springer Science & Business Media ISBN 13 :9401720436 Total Pages :339 pages Book Rating :4.4/5 (17 download)
Book Synopsis Language, Quantum, Music by : Maria Luisa Dalla Chiara
Download or read book Language, Quantum, Music written by Maria Luisa Dalla Chiara and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: A vivid and comprehensive picture of the current state of research in all directions of logic and philosophy of science. The book presents a wide combination of papers containing relevant technical results in the foundations of science and papers devoted to conceptual analyses, deeply rooted in advanced present-day research. Audience: The volume is attractive both for specialists in foundational questions and scholars interested in general epistemology.
Book Synopsis Open Quantum Systems by : Subhashish Banerjee
Download or read book Open Quantum Systems written by Subhashish Banerjee and published by Springer. This book was released on 2018-11-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.
Download or read book Persons written by Peter van Inwagen and published by Clarendon Press. This book was released on 2007-01-25 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nature of persons is a perennial topic of debate in philosophy, currently enjoying something of a revival. In this volume for the first time metaphysical debates about the nature of human persons are brought together with related debates in philosophy of religion and theology. Fifteen specially written essays explore idealist, dualist, and materialist views of persons, discuss specifically Christian conceptions of the value of embodiment, and address four central topics in philosophical theology: incarnation, resurrection, original sin, and the trinity.
Book Synopsis Quantum Communications and Measurement by : V.P. Belavkin
Download or read book Quantum Communications and Measurement written by V.P. Belavkin and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Workshop on Quantum Communications and Measurement was held at the University of Nottingham from July 10-16, 1994. It followed the successful meeting on Quantum Aspects of Optical Communications in Paris in November 1990. This time the conference was devoted to mathematical, physical and engineering aspects of quantum noise, signal processing and quantum informa tion in open systems, quantum channels, and optical communications. It brought research workers in the experimental and engineering aspects of quantum optics and communication systems into contact with theoreticians working in quantum probability and measurement theory. The workshop was attended by more than 130 participants from 22 different countries. The largest groups [after the UK (31)] were from Japan (19) and from Russia (14). The subjects discussed included the mathematical foundations of quantum communication systems, experiments and devices, the problem of collapse and continuous measurement, quantum input and output processes, causality and nondemolition observation, squeezed states, quan tum jumps, state diffusion and spontaneous localization, filtering and control in quantum systems, and new quantum optical phenomena and effects, including non classical light. These new mathematical and physical ideas were stimulated by recent advances in generation and detection of light with low quantum noise and the development of techniques for trapping a single atom over an extended period of time, making it possible to observe individual quantum phenomena at the macroscopic level.
Book Synopsis Quantum Mechanics In Phase Space: An Overview With Selected Papers by : Thomas L Curtright
Download or read book Quantum Mechanics In Phase Space: An Overview With Selected Papers written by Thomas L Curtright and published by World Scientific. This book was released on 2005-12-09 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.
Book Synopsis Coherent States, Wavelets and Their Generalizations by : Syed T. Ali
Download or read book Coherent States, Wavelets and Their Generalizations written by Syed T. Ali and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows the group context to be dispensed with altogether. The unified background makes transparent otherwise obscure properties of wavelets and of coherent states. Many concrete examples, such as semisimple Lie groups, the relativity group, and several kinds of wavelets, are discussed in detail. The book concludes with physical applications, centering on the quantum measurement problem and the quantum-classical transition. Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self- contained. With its extensive references to the research literature, the book will also be a useful compendium of recent results for physicists and mathematicians already active in the field.
Book Synopsis Quantum Bioinformatics Four by : Luigi Accardi
Download or read book Quantum Bioinformatics Four written by Luigi Accardi and published by World Scientific. This book was released on 2011 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this proceedings volume is to return to the starting point of bio-informatics and quantum information, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics, physics, information and life sciences, in particular, research for new paradigm for information science and life science on the basis of quantum theory.
Book Synopsis New Perspectives On Einstein's E = Mc2 by : Young Suh Kim
Download or read book New Perspectives On Einstein's E = Mc2 written by Young Suh Kim and published by World Scientific. This book was released on 2018-09-18 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's energy-momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of light. If one formula or formalism is applicable to all speeds, we say it is 'Lorentz-covariant.' As for the internal space-time symmetries, there does not appear to be a clear way to approach this problem. For a particle at rest, there are three spin degrees of freedom. For a massless particle, there are helicity and gauge degrees of freedom. The aim of this book is to present one Lorentz-covariant picture of these two different space-time symmetries. Using the same mathematical tool, it is possible to give a Lorentz-covariant picture of Gell-Mann's quark model for the proton at rest and Feynman's parton model for the fast-moving proton. The mathematical formalism for these aspects of the Lorentz covariance is based on two-by-two matrices and harmonic oscillators which serve as two basic scientific languages for many different branches of physics. It is pointed out that the formalism presented in this book is applicable to various aspects of optical sciences of current interest.
