LEADER 02990nam 2200553 450 001 9910554219503321 005 20230629233258.0 010 $a3-11-072277-1 010 $a9783110722772$b(electronic bk.) 010 $a3110722771$b(electronic book) 024 7 $a10.1515/9783110722772 035 $a(CKB)5590000000532555 035 $a(OCoLC)1262308303 035 $a(DE-B1597)571077 035 $a(DE-B1597)9783110722772 035 $a(MiAaPQ)EBC6702239 035 $a(Au-PeEL)EBL6702239 035 $a(EXLCZ)995590000000532555 100 $a20220430d2021 uy 0 101 0 $aeng 135 $aur||#|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuantum harmonic analysis $ean introduction /$fMaurice A. de Gosson 210 1$aBoston, Massachusetts :$cDe Gruyter,$d[2021] 210 4$dİ2021 215 $a1 online resource (xviii, 222 pages) 225 0 $aAdvances in analysis and geometry ;$vvolume 4 311 1 $a3-11-072261-5 311 08$aPrint version: 9783110722901 311 08$aPrint version: 9783110722611 320 $aIncludes bibliographical references and index. 327 $tFrontmatter --$tContents --$tPreface --$tIntroduction --$t1 Preliminaries --$t2 Displacements and reflections --$t3 The cross-Wigner transform --$t4 Gaussians and hermite functions --$t5 The Weyl transform --$t6 The Cohen class --$t7 Born?Jordan quantization --$t8 Metaplectic operators --$t9 The property of symplectic covariance --$t10 The Feichtinger algebra --$t11 Hilbert?Schmidt operators --$t12 The trace class --$t13 The quantum Bochner theorem --$t14 The density operator --$t15 The uncertainty principle --$t16 Separability and entanglement --$t17 Separability of Gaussian states --$tBibliography --$tIndex 330 $aQuantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers. 410 0$aAdvances in analysis and geometry ;$v4. 606 $aQuantum theory 606 $aHarmonic analysis 615 0$aQuantum theory. 615 0$aHarmonic analysis. 676 $a530.12 700 $aGosson$b Maurice de$067588 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910554219503321 996 $aQuantum harmonic analysis$92818754 997 $aUNINA