Quantum Harmonic Analysis
An Introduction
1st Edition
Published on 5. July 2021
XVIII, 222 pages
978-3-11-072277-2 (ISBN)
Description
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.
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Book
07/2021
1st Edition
De Gruyter
€179.95
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07/2021
1st Edition
De Gruyter
€179.95
Available for download
Person
Maurice A. de Gosson
, University of Vienna, Vienna, Austria.
Content
- Intro
- Contents
- Preface
- Introduction
- 1 Preliminaries
- 2 Displacements and reflections
- 3 The cross-Wigner transform
- 4 Gaussians and hermite functions
- 5 The Weyl transform
- 6 The Cohen class
- 7 Born-Jordan quantization
- 8 Metaplectic operators
- 9 The property of symplectic covariance
- 10 The Feichtinger algebra
- 11 Hilbert-Schmidt operators
- 12 The trace class
- 13 The quantum Bochner theorem
- 14 The density operator
- 15 The uncertainty principle
- 16 Separability and entanglement
- 17 Separability of Gaussian states
- Bibliography
- Index
