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The Wigner Transform
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Author :Maurice A De Gosson Publisher :World Scientific Publishing Company ISBN 13 :1786343118 Total Pages :250 pages Book Rating :4.7/5 (863 download)
Book Synopsis The Wigner Transform by : Maurice A De Gosson
Download or read book The Wigner Transform written by Maurice A De Gosson and published by World Scientific Publishing Company. This book was released on 2017-03-17 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform.Written for advanced-level students and professors in mathematics and mathematical physics, it is designed as a complete textbook course providing analysis on the most important research on the subject to date. Due to the advanced nature of the content, it is also suitable for research mathematicians, engineers and chemists active in the field.
Book Synopsis The Wigner Transform by : Maurice A. De Gosson
Download or read book The Wigner Transform written by Maurice A. De Gosson and published by . This book was released on 2017 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Microlocal and Time-Frequency Analysis by : Paolo Boggiatto
Download or read book Advances in Microlocal and Time-Frequency Analysis written by Paolo Boggiatto and published by Springer Nature. This book was released on 2020-03-03 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.
Book Synopsis The Wigner Distribution by : W. Mecklenbräuker
Download or read book The Wigner Distribution written by W. Mecklenbräuker and published by . This book was released on 1997-10-08 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seven contributions discuss in depth several aspects of one of the methods for representing both the frequency domain and the temporal localization of signals, which has tremendous importance in signal analysis and processing. Among them are properties like positivity, spread, and interference-term geometry; signal synthesis methods and their application to signal design, time- frequency filtering, and signal separation; the analysis of non- stationary random processes; singular value decompositions and their application to detection and classification; and optical applications of the Wigner Distribution. Also includes a bibliography of published works on the subject from 1985 to 1992. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Weyl Transforms written by M.W. Wong and published by Springer Science & Business Media. This book was released on 2006-03-31 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the functional analytic properties of Weyl transforms as bounded linear operators on $ L2ü(äBbb Rünü) $ in terms of the symbols of the transforms. Further, the boundedness, the compactness, the spectrum and the functional calculus of the Weyl transform are proved in detail, while new results and techniques on the boundedness and compactness of the Weyl transforms in terms of the symbols in $ Lrü(äBbb Rü2nü) $ and in terms of the Wigner transforms of Hermite functions are given. The roles of the Heisenberg group and the symplectic group in the study of the structure of the Weyl transform are explained, and the connections of the Weyl transform with quantization are highlighted throughout the book. Localisation operators, first studied as filters in signal analysis, are shown to be Weyl transforms with symbols expressed in terms of the admissible wavelets of the localisation operators. The results and methods mean this book is of interest to graduates and mathematicians working in Fourier analysis, operator theory, pseudo-differential operators and mathematical physics.
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.
Book Synopsis Wavelet Transforms and Their Applications by : Lokenath Debnath
Download or read book Wavelet Transforms and Their Applications written by Lokenath Debnath and published by Springer. This book was released on 2014-11-25 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.
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 The Wigner Function in Science and Technology by : David K. Ferry
Download or read book The Wigner Function in Science and Technology written by David K. Ferry and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is designed to give a background on the origins and development of Wigner functions, as well as its mathematical underpinnings. Along the way the authors emphasise the connections, and differences, from the more popular non-equilibrium Green's function approaches. But, the importance of the text lies in the discussions of the applications of the Wigner function in various fields of science, including quantum information, coherent optics, and superconducting qubits. These disciplines approach it differently, and the goal here is to give a unified background and highlight how it is utilized in the different disciplines." -- Prové de l'editor.
Book Synopsis Mathematical Aspects Of Weyl Quantization And Phase by : Daniel Abrom Dubin
Download or read book Mathematical Aspects Of Weyl Quantization And Phase written by Daniel Abrom Dubin and published by World Scientific. This book was released on 2000-06-12 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes in considerable generality the quantization-dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories. It features: a thorough treatment of quantization in polar coordinates; dequantization by a new method of “motes”; a discussion of Moyal algebras; modifications of the transform method to accommodate operator orderings; a rigorous discussion of the Dicke laser model for one mode, fully quantum, in the thermodynamic limit; analysis of quantum phase theories based on the Toeplitz operator, the coherent state operator, the quantized phase space angle, and a sequence of finite rank operators.
Book Synopsis Applications in Time-Frequency Signal Processing by : Antonia Papandreou-Suppappola
Download or read book Applications in Time-Frequency Signal Processing written by Antonia Papandreou-Suppappola and published by CRC Press. This book was released on 2018-10-03 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because most real-world signals, including speech, sonar, communication, and biological signals, are non-stationary, traditional signal analysis tools such as Fourier transforms are of limited use because they do not provide easily accessible information about the localization of a given frequency component. A more suitable approach for those studying non-stationary signals is the use of time frequency representations that are functions of both time and frequency. Applications in Time-Frequency Signal Processing investigates the use of various time-frequency representations, such as the Wigner distribution and the spectrogram, in diverse application areas. Other books tend to focus on theoretical development. This book differs by highlighting particular applications of time-frequency representations and demonstrating how to use them. It also provides pseudo-code of the computational algorithms for these representations so that you can apply them to your own specific problems. Written by leaders in the field, this book offers the opportunity to learn from experts. Time-Frequency Representation (TFR) algorithms are simplified, enabling you to understand the complex theories behind TFRs and easily implement them. The numerous examples and figures, review of concepts, and extensive references allow for easy learning and application of the various time-frequency representations.
Download or read book Weyl Transforms written by M.W. Wong and published by Springer Science & Business Media. This book was released on 1998-08-21 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the functional analytic properties of Weyl transforms as bounded linear operators on $ L2ü(äBbb Rünü) $ in terms of the symbols of the transforms. Further, the boundedness, the compactness, the spectrum and the functional calculus of the Weyl transform are proved in detail, while new results and techniques on the boundedness and compactness of the Weyl transforms in terms of the symbols in $ Lrü(äBbb Rü2nü) $ and in terms of the Wigner transforms of Hermite functions are given. The roles of the Heisenberg group and the symplectic group in the study of the structure of the Weyl transform are explained, and the connections of the Weyl transform with quantization are highlighted throughout the book. Localisation operators, first studied as filters in signal analysis, are shown to be Weyl transforms with symbols expressed in terms of the admissible wavelets of the localisation operators. The results and methods mean this book is of interest to graduates and mathematicians working in Fourier analysis, operator theory, pseudo-differential operators and mathematical physics.
Book Synopsis Born-Jordan Quantization by : Maurice A. de Gosson
Download or read book Born-Jordan Quantization written by Maurice A. de Gosson and published by Springer. This book was released on 2016-01-11 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive mathematical study of the operators behind the Born–Jordan quantization scheme. The Schrödinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born–Jordan scheme is used. Thus, Born–Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born–Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.
Book Synopsis Foundations of Time-Frequency Analysis by : Karlheinz Gröchenig
Download or read book Foundations of Time-Frequency Analysis written by Karlheinz Gröchenig and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
Book Synopsis Physics of Submicron Devices by : David K. Ferry
Download or read book Physics of Submicron Devices written by David K. Ferry and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purposes of this book are many. First, we must point out that it is not a device book, as a proper treatment of the range of important devices would require a much larger volume even without treating the important physics for submicron devices. Rather, the book is written principally to pull together and present in a single place, and in a (hopefully) uniform treatment, much of the understanding on relevant physics for submicron devices. Indeed, the understand ing that we are trying to convey through this work has existed in the literature for quite some time, but has not been brought to the full attention of those whose business is the making of submicron devices. It should be remarked that much of the important physics that is discussed here may not be found readily in devices at the 1.0-JLm level, but will be found to be dominant at the O.I-JLm level. The range between these two is rapidly being covered as technology moves from the 256K RAM to the 16M RAM chips.
Book Synopsis Mathematical Aspects of Weyl Quantization and Phase by : D. A. Dubin
Download or read book Mathematical Aspects of Weyl Quantization and Phase written by D. A. Dubin and published by World Scientific. This book was released on 2000 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes in considerable generality the quantization-dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories. It features: a thorough treatment of quantization in polar coordinates; dequantization by a new method of "motes"; a discussion of Moyal algebras; modifications of the transform method to accommodate operator orderings; a rigorous discussion of the Dieke laser model for one mode, fully quantum, in the thermodynamic limit; analysis of quantum phase theories based on the Toeplitz operator, the coherent state operator, the quantized phase space angle, and a sequence of finite rank operators.
