Born Jordan Quantization
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Born Jordan Quantization
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Author : Maurice A. de Gosson
language : en
Publisher: Springer
Release Date : 2016-01-11
Born Jordan Quantization written by Maurice A. de Gosson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-11 with Science categories.
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.
Quantum Harmonic Analysis
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Author : Maurice A. de Gosson
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-07-05
Quantum Harmonic Analysis written by Maurice A. de Gosson and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Mathematics categories.
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.
Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics
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Author : Gianfausto Dell'Antonio
language : en
Publisher: Springer
Release Date : 2016-05-24
Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics written by Gianfausto Dell'Antonio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-24 with Science categories.
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.
Excursions In Harmonic Analysis Volume 6
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Author : Matthew Hirn
language : en
Publisher: Springer Nature
Release Date : 2021-09-01
Excursions In Harmonic Analysis Volume 6 written by Matthew Hirn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-01 with Mathematics categories.
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.
Time Frequency Analysis Of Operators
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Author : Elena Cordero
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-09-21
Time Frequency Analysis Of Operators written by Elena Cordero and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-21 with Mathematics categories.
This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.
Quantum Theory
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Author : Peter Bongaarts
language : en
Publisher: Springer
Release Date : 2014-12-01
Quantum Theory written by Peter Bongaarts and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with Science categories.
This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.
Generalized Functions And Fourier Analysis
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Author : Michael Oberguggenberger
language : en
Publisher: Birkhäuser
Release Date : 2017-05-06
Generalized Functions And Fourier Analysis written by Michael Oberguggenberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-06 with Mathematics categories.
This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.
Principles Of Newtonian And Quantum Mechanics The The Need For Planck S Constant H Second Edition
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Author : Maurice A De Gosson
language : en
Publisher: World Scientific
Release Date : 2016-11-10
Principles Of Newtonian And Quantum Mechanics The The Need For Planck S Constant H Second Edition written by Maurice A De Gosson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-10 with Science categories.
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.
Commutation Relations Normal Ordering And Stirling Numbers
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Author : Toufik Mansour
language : en
Publisher: CRC Press
Release Date : 2015-09-18
Commutation Relations Normal Ordering And Stirling Numbers written by Toufik Mansour and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
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
Landscapes Of Time Frequency Analysis
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Author : Paolo Boggiatto
language : en
Publisher: Springer Nature
Release Date : 2020-11-21
Landscapes Of Time Frequency Analysis written by Paolo Boggiatto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Mathematics categories.
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.