LEADER 05386nam 22008295 450 001 9910438157903321 005 20200701011447.0 010 $a9781489993625 010 $a9781461471165 (ebook) 010 $a0072-5285 (ISSN) 024 7 $a10.1007/978-1-4614-7116-5 035 $a(CKB)2670000000393918 035 $a(EBL)1317525 035 $a(OCoLC)870244209 035 $a(SSID)ssj0000936062 035 $a(PQKBManifestationID)11948070 035 $a(PQKBTitleCode)TC0000936062 035 $a(PQKBWorkID)10961345 035 $a(PQKB)10614493 035 $a(DE-He213)978-1-4614-7116-5 035 $a(MiAaPQ)EBC1317525 035 $a(Au-PeEL)EBL1317525 035 $a(CaPaEBR)ebr10983436 035 $a(PPN)17048842X 035 $a(EXLCZ)992670000000393918 100 $a20130619d2013 u| 0 101 0 $aeng 181 $ctxt$2rdacontent 182 $cn$2rdamedia 183 $anc$2rdacarrier 200 10$aQuantum Theory for Mathematicians /$fby Brian C. Hall 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $aXVI, 554 p. $cgráf. ;$d24 cm 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v267 320 $aIncluye referencias bibliográficas (p. 545-548) e índice 327 $a1 The Experimental Origins of Quantum Mechanics -- 2 A First Approach to Classical Mechanics -- 3 A First Approach to Quantum Mechanics -- 4 The Free Schrödinger Equation -- 5 A Particle in a Square Well -- 6 Perspectives on the Spectral Theorem -- 7 The Spectral Theorem for Bounded Self-Adjoint Operators: Statements -- 8 The Spectral Theorem for Bounded Sef-Adjoint Operators: Proofs -- 9 Unbounded Self-Adjoint Operators -- 10 The Spectral Theorem for Unbounded Self-Adjoint Operators -- 11 The Harmonic Oscillator -- 12 The Uncertainty Principle -- 13 Quantization Schemes for Euclidean Space -- 14 The Stone?von Neumann Theorem -- 15 The WKB Approximation -- 16 Lie Groups, Lie Algebras, and Representations -- 17 Angular Momentum and Spin -- 18 Radial Potentials and the Hydrogen Atom -- 19 Systems and Subsystems, Multiple Particles -- V Advanced Topics in Classical and Quantum Mechanics -- 20 The Path-Integral Formulation of Quantum Mechanics -- 21 Hamiltonian Mechanics on Manifolds -- 22 Geometric Quantization on Euclidean Space -- 23 Geometric Quantization on Manifolds -- A Review of Basic Material -- References. - Index. 330 $aAlthough ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone?von Neumann Theorem; the Wentzel?Kramers?Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces.  The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v267 606 $aMathematical physics 606 $aQuantum physics 606 $aFunctional analysis 606 $aTopological groups 606 $aLie groups 606 $aPhysics 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 615 0$aMathematical physics. 615 0$aQuantum physics. 615 0$aFunctional analysis. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aPhysics. 615 14$aMathematical Physics. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aQuantum Physics. 615 24$aFunctional Analysis. 615 24$aTopological Groups, Lie Groups. 615 24$aMathematical Methods in Physics. 676 $a530.12 700 $aHall$b Brian C$4aut$4http://id.loc.gov/vocabulary/relators/aut$0149974 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438157903321 996 $aQuantum theory for mathematicians$9836756 997 $aUNINA