The Weyl Operator And Its Generalization

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The Weyl Operator and its Generalization

Leon Cohen
The Weyl Operator and its Generalization Book PDF

Author : Leon Cohen
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 49,7 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034802949

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The Weyl Operator and its Generalization by Leon Cohen Pdf

The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar. This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner.

Advances in Microlocal and Time-Frequency Analysis

Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler
Advances in Microlocal and Time Frequency Analysis Book PDF

Author : Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler
Publisher : Springer Nature
Page : 533 pages
File Size : 51,8 Mb
Release : 2020-03-03
Category : Mathematics
ISBN : 9783030361389

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Advances in Microlocal and Time-Frequency Analysis by Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler Pdf

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.

Quantum Harmonic Analysis

Maurice A. de Gosson
Quantum Harmonic Analysis Book PDF

Author : Maurice A. de Gosson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 240 pages
File Size : 54,6 Mb
Release : 2021-07-05
Category : Mathematics
ISBN : 9783110722772

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Quantum Harmonic Analysis by Maurice A. de Gosson Pdf

Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.

Commutation Relations, Normal Ordering, and Stirling Numbers

Toufik Mansour,Matthias Schork
Commutation Relations Normal Ordering and Stirling Numbers Book PDF

Author : Toufik Mansour,Matthias Schork
Publisher : CRC Press
Page : 506 pages
File Size : 41,9 Mb
Release : 2015-09-18
Category : Mathematics
ISBN : 9781466579897

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Commutation Relations, Normal Ordering, and Stirling Numbers by Toufik Mansour,Matthias Schork Pdf

Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow

Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes

De Gosson Maurice A
Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes Book PDF

Author : De Gosson Maurice A
Publisher : World Scientific
Page : 308 pages
File Size : 46,9 Mb
Release : 2017-11-10
Category : Science
ISBN : 9781786344168

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Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes by De Gosson Maurice A Pdf

The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical. Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field. Contents: Hamiltonian MechanicsHamilton–Jacobi TheoryMatter Waves, Schrödinger's Equation, and Bohm's Theory The MetatronUncertainties and Quantum BlobsQuantum States and the Density MatrixVarying Planck's ConstantAppendices: The Symplectic GroupThe Metaplectic RepresentationBorn–Jordan QuantizationTwisted Product and Convolution Readership: Undergraduate and graduate students of mathematics and physics, interested in analysis and differential equations, probability and statistics, geometry and topology and mathematical physics. Keywords: Classical Mechanics;Hamiltonian Mechanics;Quantum Mechanics;Planck's Constant;Mathematical Physics;Algebraic GeometryReview:0

Landscapes of Time-Frequency Analysis

Paolo Boggiatto,Tommaso Bruno,Elena Cordero,Hans G. Feichtinger,Fabio Nicola,Alessandro Oliaro,Anita Tabacco,Maria Vallarino
Landscapes of Time Frequency Analysis Book PDF

Author : Paolo Boggiatto,Tommaso Bruno,Elena Cordero,Hans G. Feichtinger,Fabio Nicola,Alessandro Oliaro,Anita Tabacco,Maria Vallarino
Publisher : Springer Nature
Page : 208 pages
File Size : 41,6 Mb
Release : 2020-11-21
Category : Mathematics
ISBN : 9783030560058

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Landscapes of Time-Frequency Analysis by Paolo Boggiatto,Tommaso Bruno,Elena Cordero,Hans G. Feichtinger,Fabio Nicola,Alessandro Oliaro,Anita Tabacco,Maria Vallarino Pdf

This contributed volume features chapters based on talks given at the second international conference titled Aspects of Time-Frequency Analysis (ATFA 19), held at Politecnico di Torino from June 25th to June 27th, 2019. Written by experts in harmonic analysis and its applications, these chapters provide a valuable overview of the state-of-the-art of this active area of research. New results are collected as well, making this a valuable resource for readers seeking to be brought up-to-date. Topics covered include: Signal analysis Quantum theory Modulation space theory Applications to the medical industry Wavelet transform theory Anti-Wick operators Landscapes of Time-Frequency Analysis: ATFA 2019 will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.

Joseph Fourier 250th Birthday

Frédéric Barbaresco,Jean-Pierre Gazeau
Joseph Fourier 250th Birthday Book PDF

Author : Frédéric Barbaresco,Jean-Pierre Gazeau
Publisher : MDPI
Page : 260 pages
File Size : 54,7 Mb
Release : 2019-03-28
Category : Science
ISBN : 9783038977469

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Joseph Fourier 250th Birthday by Frédéric Barbaresco,Jean-Pierre Gazeau Pdf

For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for non-commutative harmonic analysis, applied to locally-compact, non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. In parallel, in geometric mechanics, Jean-Marie Souriau interpreted the temperature vector of Planck as a space-time vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring non-commutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.

Analysis of Pseudo-Differential Operators

Shahla Molahajloo,M. W. Wong
Analysis of Pseudo Differential Operators Book PDF

Author : Shahla Molahajloo,M. W. Wong
Publisher : Springer
Page : 257 pages
File Size : 40,8 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9783030051686

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Analysis of Pseudo-Differential Operators by Shahla Molahajloo,M. W. Wong Pdf

This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.

Born-Jordan Quantization

Maurice A. de Gosson
Born Jordan Quantization Book PDF

Author : Maurice A. de Gosson
Publisher : Springer
Page : 226 pages
File Size : 46,8 Mb
Release : 2016-01-11
Category : Science
ISBN : 9783319279022

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Born-Jordan Quantization by Maurice A. de Gosson Pdf

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.

Annual Reports on Computational Chemistry

David A. Dixon
Annual Reports on Computational Chemistry Book PDF

Author : David A. Dixon
Publisher : Elsevier
Page : 200 pages
File Size : 47,8 Mb
Release : 2020-09-24
Category : Science
ISBN : 9780128206959

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Annual Reports on Computational Chemistry by David A. Dixon Pdf

Annual Reports in Computational Chemistry, Volume 16, provides timely and critical reviews of important topics in computational chemistry. Topics covered in this series include quantum chemistry, molecular mechanics, force fields, chemical education, and applications in academic and industrial settings. Focusing on the most recent literature and advances in the field, each article covers a specific topic of importance to computational chemists. Includes timely discussions on quantum chemistry and molecular mechanics Covers force fields, chemical education, and more Presents the latest in chemical education and applications in both academic and industrial settings

Active Flow and Combustion Control 2018

Rudibert King
Active Flow and Combustion Control 2018 Book PDF

Author : Rudibert King
Publisher : Springer
Page : 380 pages
File Size : 52,6 Mb
Release : 2018-09-03
Category : Technology & Engineering
ISBN : 9783319981772

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Active Flow and Combustion Control 2018 by Rudibert King Pdf

The book reports on the latest theoretical and experimental findings in the field of active flow and combustion control. It covers new developments in actuator technology and sensing, in robust and optimal open- and closed-loop control, as well as in model reduction for control, constant volume combustion and dynamic impingement cooling. The chapters reports oncutting-edge contributions presented during the fourth edition of the Active Flow and Combustion Control conference, held in September 19 to 21, 2018 at the Technische Universität Berlin, in Germany. This conference, as well as the research presented in the book, have been supported by the collaborative research center SFB 1029 on “Substantial efficiency increase in gas turbines through direct use of coupled unsteady combustion and flow dynamics”, funded by the DFG (German Research Foundation). It offers a timely guide for researchers and practitioners in the field of aeronautics, turbomachinery, control and combustion.

Wave Packet Analysis of Feynman Path Integrals

Fabio Nicola,S. Ivan Trapasso
Wave Packet Analysis of Feynman Path Integrals Book PDF

Author : Fabio Nicola,S. Ivan Trapasso
Publisher : Springer Nature
Page : 220 pages
File Size : 46,9 Mb
Release : 2022-07-28
Category : Science
ISBN : 9783031061868

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Wave Packet Analysis of Feynman Path Integrals by Fabio Nicola,S. Ivan Trapasso Pdf

The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.

Excursions in Harmonic Analysis, Volume 6

Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz
Excursions in Harmonic Analysis Volume 6 Book PDF

Author : Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz
Publisher : Springer Nature
Page : 444 pages
File Size : 47,5 Mb
Release : 2021-09-01
Category : Mathematics
ISBN : 9783030696375

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Excursions in Harmonic Analysis, Volume 6 by Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz Pdf

John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.

Generalized Fractional Calculus and Applications

Virginia S Kiryakova
Generalized Fractional Calculus and Applications Book PDF

Author : Virginia S Kiryakova
Publisher : CRC Press
Page : 412 pages
File Size : 55,7 Mb
Release : 1993-12-27
Category : Mathematics
ISBN : 0582219779

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Generalized Fractional Calculus and Applications by Virginia S Kiryakova Pdf

In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.

Strings, Conformal Fields, and M-Theory

Michio Kaku
Strings Conformal Fields and M Theory Book PDF

Author : Michio Kaku
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461205036

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Strings, Conformal Fields, and M-Theory by Michio Kaku Pdf

Building on the foundations laid in his Introduction to Superstrings and M Theory, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, and the insights into 11-dimensional strings recently obtained from M-theory. New chapters discuss such topics as Seiberg-Witten theory, M theory and duality, and D-branes. Throughout, the author conveys the vitality of the current research and places readers at its forefront. Several chapters reviewing the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum.