Quantum Harmonic Analysis PDF Download
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Author | : Maurice A. de Gosson |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 247 |
Release | : 2021-07-05 |
Genre | : Mathematics |
ISBN | : 3110722909 |
Download Quantum Harmonic Analysis Book in PDF, ePub and Kindle
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.
Author | : Maurice A. de Gosson |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 240 |
Release | : 2021-07-05 |
Genre | : Mathematics |
ISBN | : 3110722771 |
Download Quantum Harmonic Analysis Book in PDF, ePub and Kindle
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.
Author | : N.E. Hurt |
Publisher | : Springer Science & Business Media |
Total Pages | : 362 |
Release | : 1982-12-31 |
Genre | : Mathematics |
ISBN | : 9789027714268 |
Download Geometric Quantization in Action Book in PDF, ePub and Kindle
Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.
Author | : Maurice A. de Gosson |
Publisher | : Springer Science & Business Media |
Total Pages | : 351 |
Release | : 2011-07-30 |
Genre | : Mathematics |
ISBN | : 3764399929 |
Download Symplectic Methods in Harmonic Analysis and in Mathematical Physics Book in PDF, ePub and Kindle
The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
Author | : V. K. Dobrev |
Publisher | : Springer |
Total Pages | : 283 |
Release | : 1977-04-01 |
Genre | : Science |
ISBN | : 9783540081500 |
Download Harmonic Analysis Book in PDF, ePub and Kindle
Author | : Norman Hurt |
Publisher | : Math Science Press |
Total Pages | : 266 |
Release | : 1980 |
Genre | : Mathematics |
ISBN | : |
Download Quantum Statistical Mechanics and Lie Group Harmonic Analysis Book in PDF, ePub and Kindle
Author | : N.E. Hurt |
Publisher | : Springer Science & Business Media |
Total Pages | : 351 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400969635 |
Download Geometric Quantization in Action Book in PDF, ePub and Kindle
Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.
Author | : Sundaram Thangavelu |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461217725 |
Download Harmonic Analysis on the Heisenberg Group Book in PDF, ePub and Kindle
The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.
Author | : Gerald B. Folland |
Publisher | : Princeton University Press |
Total Pages | : 288 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400882427 |
Download Harmonic Analysis in Phase Space. (AM-122), Volume 122 Book in PDF, ePub and Kindle
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.
Author | : Paolo Boggiatto |
Publisher | : Springer Nature |
Total Pages | : 208 |
Release | : 2020-11-21 |
Genre | : Mathematics |
ISBN | : 3030560058 |
Download Landscapes of Time-Frequency Analysis Book in PDF, ePub and Kindle
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.