02990nam 2200553 450 991055421950332120230629233258.03-11-072277-19783110722772(electronic bk.)3110722771(electronic book)10.1515/9783110722772(CKB)5590000000532555(OCoLC)1262308303(DE-B1597)571077(DE-B1597)9783110722772(MiAaPQ)EBC6702239(Au-PeEL)EBL6702239(EXLCZ)99559000000053255520220430d2021 uy 0engur||#||||||||txtrdacontentcrdamediacrrdacarrierQuantum harmonic analysis an introduction /Maurice A. de GossonBoston, Massachusetts :De Gruyter,[2021]©20211 online resource (xviii, 222 pages)Advances in analysis and geometry ;volume 43-11-072261-5 Print version: 9783110722901 Print version: 9783110722611 Includes bibliographical references and index.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 --IndexQuantum 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.Advances in analysis and geometry ;4.Quantum theoryHarmonic analysisQuantum theory.Harmonic analysis.530.12Gosson Maurice de67588MiAaPQMiAaPQMiAaPQBOOK9910554219503321Quantum harmonic analysis2818754UNINA