LEADER 04313nam 22006975 450 001 9910257443603321 005 20200702021138.0 010 $a3-540-46859-5 024 7 $a10.1007/3-540-51916-5 035 $a(CKB)1000000000233475 035 $a(SSID)ssj0000322641 035 $a(PQKBManifestationID)12106193 035 $a(PQKBTitleCode)TC0000322641 035 $a(PQKBWorkID)10289392 035 $a(PQKB)11200615 035 $a(DE-He213)978-3-540-46859-2 035 $a(PPN)155173014 035 $a(EXLCZ)991000000000233475 100 $a20121227d1989 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDirac Kets, Gamow Vectors and Gel?fand Triplets$b[electronic resource] $eThe Rigged Hilbert Space Formulation of Quantum Mechanics. Lectures in Mathematical Physics at the University of Texas at Austin /$fby Arno Bohm, Manuel Gadella ; edited by Arno Bohm, J.D. Dollard 205 $a1st ed. 1989. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1989. 215 $a1 online resource (VIII, 120 p.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v348 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-51916-5 327 $aI. The algebraic structure of the space of states -- II. The topological structure of the space of states -- III. The conjugate space of ? -- IV. Generalized eigenvectors and the nuclear spectral theorem -- V. A remark concerning generalization -- References on chapter I -- II. The Moller wave operators -- III. The Hardy class functions on a half plane -- References for chapter II -- I. Rigged Hilbert spaces of Hardy class functions -- II. The spaces ?+ and ?? -- III. Functional for Ho and Hl -- References for chapter III -- I. The RHS model for decaying states -- II. Dynamical semigroups -- III. Virtual states -- References for chapter IV. 330 $aDirac's formalism of quantum mechanics was always praised for its elegance. This book introduces the student to its mathematical foundations and demonstrates its ease of applicability to problems in quantum physics. The book starts by describing in detail the concept of Gel'fand triplets and how one can make use of them to make the Dirac heuristic approach rigorous. The results are then deepened by giving the analytic tools, such as the Hardy class function and Hilbert and Mellin transforms, needed in applications to physical problems. Next, the RHS model for decaying states based on the concept of Gamow vectors is presented. Applications are given to physical theories of such phenomena as decaying states and resonances. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v348 606 $aPhysics 606 $aElementary particles (Physics) 606 $aQuantum field theory 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 606 $aElementary Particles, Quantum Field Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P23029 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aPhysics. 615 0$aElementary particles (Physics). 615 0$aQuantum field theory. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aMathematical Methods in Physics. 615 24$aNumerical and Computational Physics, Simulation. 615 24$aElementary Particles, Quantum Field Theory. 615 24$aAnalysis. 676 $a530.15 700 $aBohm$b Arno$4aut$4http://id.loc.gov/vocabulary/relators/aut$040451 702 $aGadella$b Manuel$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aBohm$b Arno$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aDollard$b J.D$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910257443603321 996 $aDirac Kets, Gamow Vectors and Gel'fand Triplets$9335479 997 $aUNINA