The Physics Of Phase Space
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Quantum Mechanics In Phase Space
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Author : Cosmas Zachos
language : en
Publisher: World Scientific
Release Date : 2005
Quantum Mechanics In Phase Space written by Cosmas Zachos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
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.
Phase Space Picture Of Quantum Mechanics
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Author : Y. S. Kim
language : en
Publisher: World Scientific
Release Date : 1991
Phase Space Picture Of Quantum Mechanics written by Y. S. Kim and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Science categories.
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.
Particle Accelerator Physics I
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Author : Helmut Wiedemann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Particle Accelerator Physics I written by Helmut Wiedemann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In this second edition of Particle Accelerator Physics, Vol. 1, is mainly a reprint of the first edition without significant changes in content. The bibliography has been updated to include more recent progress in the field of particle accelerators. With the help of many observant readers a number of misprints and errors could be eliminated. The author would like to express his sincere appreciation to all those who have pointed out such shortcomings and wel comes such information and any other relevant information in the future. The author would also like to express his special thanks to the editor Dr. Helmut Lotsch and his staff for editorial as well as technical advice and support which contributed greatly to the broad acceptance of this text and made a second edition of both volumes necessary. Palo Alto, California Helmut Wiedemann November 1998 VII Preface to the First Edition The purpose of this textbook is to provide a comprehensive introduction into the physics of particle accelerators and particle beam dynamics. Parti cle accelerators have become important research tools in high energy physics as well as sources of incoherent and coherent radiation from the far infra red to hard x-rays for basic and applied research. During years of teaching accelerator physics it became clear that the single most annoying obstacle to get introduced into the field is the absence of a suitable textbook.
Phase Space Optics Fundamentals And Applications
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Author : Markus Testorf
language : en
Publisher: McGraw Hill Professional
Release Date : 2009-09-07
Phase Space Optics Fundamentals And Applications written by Markus Testorf and has been published by McGraw Hill Professional this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-07 with Technology & Engineering categories.
A comprehensive cross section of phase-space optics This definitive volume highlights an elegant, unified approach to optical rays, waves, and system design using cutting-edge phase-space techniques. Phase-Space Optics: Fundamentals and Applications details theoretical concepts of phase space as well as novel engineering applications in specific disciplines. This authoritative guide includes full coverage of sampling, superresolution imaging, and the phase-space interpretation of ultrafast optics. Work with Wigner optics, analyze phase-space equations, develop wave propagation models, and gain a new understanding of optical sources and systems. Discover how to: Describe optical phenomena using Wigner and ambiguity functions Perform phase-space rotations using ray transformation matrices Influence the trade-off between pupil size and depth of field Analyze and design optical signals using the Radon-Wigner transform Accomplish superresolution by squeezing phase space Interpret the intimate relationship between radiometry and coherence Use basic algebra to discover self-imaging, Fresnel diffraction, and the Talbot effect Develop discrete models, sampling criteria, and interpolation formulae Work with ultrafast processes and complex space-time structures
Harmonic Analysis In Phase Space
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Author : G. B. Folland
language : en
Publisher: Princeton University Press
Release Date : 1989-03-21
Harmonic Analysis In Phase Space written by G. B. Folland and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-21 with Mathematics categories.
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.
Galileo Unbound
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Author : David D. Nolte
language : en
Publisher: Oxford University Press
Release Date : 2018-07-12
Galileo Unbound written by David D. Nolte and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Science categories.
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once -- setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
The Symmetry Perspective
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Author : Martin Golubitsky
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Symmetry Perspective written by Martin Golubitsky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
Linear Ray And Wave Optics In Phase Space
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Author : Amalia Torre
language : en
Publisher: Elsevier
Release Date : 2020-06-01
Linear Ray And Wave Optics In Phase Space written by Amalia Torre and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-01 with Science categories.
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
Phase Space
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Author : Stephen Baxter
language : en
Publisher: HarperCollins UK
Release Date : 2012-06-28
Phase Space written by Stephen Baxter and has been published by HarperCollins UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-28 with Fiction categories.
2025. Tied in to Baxter’s masterful Manifold trilogy, these thematically linked stories are drawn from the vast graph of possibilities across which the lives of hero Reid Malenfant have been scattered.
Quantum Mechanics In Phase Space
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Author : Cosmas Zachos
language : en
Publisher: World Scientific
Release Date : 2005
Quantum Mechanics In Phase Space written by Cosmas Zachos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
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.