Quantum Harmonic Analysis : : An Introduction / / Maurice A. de Gosson.

• Superior document: Title is part of eBook package: De Gruyter DG Ebook Package English 2021
• VerfasserIn: Gosson, Maurice A. de,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2021]; ©2021
• Year of Publication: 2021
• Language: English
• Series: Advances in Analysis and Geometry , 4
• Physical Description: 1 online resource (XVIII, 222 p.)
• Other title: Frontmatter --; 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110722772; 9783110750720; 9783110750706; 9783110754001; 9783110753776; 9783110754131; 9783110753905
• ISSN: 2511-0438
• DOI: 10.1515/9783110722772
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Maurice A. de Gosson.

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.