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Quantum Harmonic Analysis

2021-07-05 Mathematics
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Release : 2021-07-05
Genre : Mathematics
Kind : eBook
Book Rating : 909/5 ( reviews)

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Book Synopsis Quantum Harmonic Analysis by : Maurice A. de Gosson

Download or read book Quantum Harmonic Analysis written by Maurice A. de Gosson. This book was released on 2021-07-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Harmonic Analysis

2021-07-05 Mathematics
Download Quantum Harmonic Analysis PDF Online Free

Author :
Release : 2021-07-05
Genre : Mathematics
Kind : eBook
Book Rating : 771/5 ( reviews)

GET EBOOK


Book Synopsis Quantum Harmonic Analysis by : Maurice A. de Gosson

Download or read book Quantum Harmonic Analysis written by Maurice A. de Gosson. This book was released on 2021-07-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Quantization in Action

1982-12-31 Mathematics
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Release : 1982-12-31
Genre : Mathematics
Kind : eBook
Book Rating : 268/5 ( reviews)

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Book Synopsis Geometric Quantization in Action by : N.E. Hurt

Download or read book Geometric Quantization in Action written by N.E. Hurt. This book was released on 1982-12-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Symplectic Methods in Harmonic Analysis and in Mathematical Physics

2011-07-30 Mathematics
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Release : 2011-07-30
Genre : Mathematics
Kind : eBook
Book Rating : 929/5 ( reviews)

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Book Synopsis Symplectic Methods in Harmonic Analysis and in Mathematical Physics by : Maurice A. de Gosson

Download or read book Symplectic Methods in Harmonic Analysis and in Mathematical Physics written by Maurice A. de Gosson. This book was released on 2011-07-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Harmonic Analysis on the Heisenberg Group

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 725/5 ( reviews)

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Book Synopsis Harmonic Analysis on the Heisenberg Group by : Sundaram Thangavelu

Download or read book Harmonic Analysis on the Heisenberg Group written by Sundaram Thangavelu. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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