Quantum Harmonic Analysis

Maurice A. de Gosson

Published by De Gruyter 2021

Quantum Harmonic Analysis

An Introduction

Maurice A. de Gosson

Volume 4 in the series Advances in Analysis and Geometry

https://doi.org/10.1515/9783110722772

Overview
Contents

About this book

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.

interesting and well-written manuscript by leading researchers

Accessible approach, written in a user and student friendly way

Author information

Maurice A. de Gosson, University of Vienna, Vienna, Austria.

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	VII
Preface Publicly Available Download PDF	XIII
Introduction Publicly Available Download PDF	XV
1 Preliminaries Requires Authentication Unlicensed Licensed Download PDF	1
2 Displacements and reflections Requires Authentication Unlicensed Licensed Download PDF	21
3 The cross-Wigner transform Requires Authentication Unlicensed Licensed Download PDF	33
4 Gaussians and hermite functions Requires Authentication Unlicensed Licensed Download PDF	49
5 The Weyl transform Requires Authentication Unlicensed Licensed Download PDF	61
6 The Cohen class Requires Authentication Unlicensed Licensed Download PDF	73
7 Born–Jordan quantization Requires Authentication Unlicensed Licensed Download PDF	83
8 Metaplectic operators Requires Authentication Unlicensed Licensed Download PDF	93
9 The property of symplectic covariance Requires Authentication Unlicensed Licensed Download PDF	103
10 The Feichtinger algebra Requires Authentication Unlicensed Licensed Download PDF	119
11 Hilbert–Schmidt operators Requires Authentication Unlicensed Licensed Download PDF	135
12 The trace class Requires Authentication Unlicensed Licensed Download PDF	145
13 The quantum Bochner theorem Requires Authentication Unlicensed Licensed Download PDF	157
14 The density operator Requires Authentication Unlicensed Licensed Download PDF	167
15 The uncertainty principle Requires Authentication Unlicensed Licensed Download PDF	181
16 Separability and entanglement Requires Authentication Unlicensed Licensed Download PDF	193
17 Separability of Gaussian states Requires Authentication Unlicensed Licensed Download PDF	205
Bibliography Requires Authentication Unlicensed Licensed Download PDF	215
Index Requires Authentication Unlicensed Licensed Download PDF	219

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate students, academic researchers.
Pages
- Front matter: 18
- Main content: 222

eBook

Published: July 5, 2021
ISBN: 9783110722772

Hardcover

Published: July 5, 2021
ISBN: 9783110722611