LEADER 07655nam a2200349 i 4500 001 991003377429707536 008 170530t2013 nyua b 001 0 eng d 020 $a9781489993625 035 $ab14324635-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a530.15$223 084 $aAMS 81-02 084 $aAMS 46N50 084 $aLC QC174.12.H346 100 1 $aHall, Brian C.,$eauthor.$0149974 245 10$aQuantum theory for mathematicians /$cBrian C. Hall. 264 1$aNew York :$bSpringer,$cc2013 300 $axvi, 554 p. :$bill. ;$c24 cm 336 $atext$btxt$2rdacontent 337 $aunmediated$bn$2rdamedia 338 $avolume$bnc$2rdacarrier 490 1 $aGraduate texts in mathematics,$x0072-5285 ;$v267 504 $aIncludes bibliographical references (pages 545-548) and index 505 00$tThe experimental origins of quantum mechanics:$tIs light a wave or a particle? ;$tIs an electron a wave or a particle? ;$tSchroÌ?dinger and Heisenberg ;$tA matter of interpretation ;$gExercises --$tA first approach to classical mechanics:$tMotion in R¹ ;$tMotion in R[superscript n] ;$tSystems of particles ;$tAngular momentum ;$tPoisson brackets and Hamiltonian mechanics ;$tThe Kepler problem and the Runge-Lenz vector ;$gExercises --$tFirst approach to quantum mechanics:$tWaves, particles, and probabilities ;$tA few words about operators and their adjoints ;$tPosition and the position operator ;$tMomentum and the momentum operator ;$tThe position and momentum operators ;$tAxioms of quantum mechanics : operators and measurements ;$tTime-evolution in quantum theory ;$tThe Heisenberg picture ;$tExample : a particle in a box ;$tQuantum mechanics for a particle in R [superscript n] ;$tSystems of multiple particles ;$tPhysics notation ;$gExercises --$tThe free SchroÌ?dinger equation:$tSolution by means of the Fourier transform ;$tSolution as a convolution ;$tPropagation of the wave packet : first approach ;$tPropagation of the wave packet : second approach ;$tSpread of the wave packet ;$gExercises --$tParticle in a square well:$tThe time-independent SchroÌ?dinger equation ;$tDomain questions and the matching conditions ;$tFinding square-integrable solutions ;$tTunneling and the classically forbidden region ;$tDiscrete and continuous spectrum ;$gExercises --$tPerspectives on the spectral theorem:$tThe difficulties with the infinite-dimensional case ;$tThe goals of spectral theory ;$tA guide to reading ;$tThe position operator ;$tMultiplication operators ;$tThe momentum operator --$tThe spectral theorem for bounded self-adjoint operators : statements:$tElementary properties of bounded operators ;$tSpectral theorem for bounded self-adjoint operators, I ;$tSpectral theorem for bounded self-adjoint operators, II ;$gExercises --$tThe spectral theorem for bounded self-adjoint operators : proofs:$tProof of the spectral theorem, first version ;$tProof of the spectral theorem, second version ;$gExercises --$tUnbounded self-adjoint operators:$gIntroduction ;$tAdjoint and closure of an unbounded operator ;$tElementary properties of adjoints and closed operators ;$tThe spectrum of an unbounded operator ;$tConditions for self-adjointness and essential self-adjointness ;$tA counterexample ;$tAn example ;$tThe basic operators of quantum mechanics ;$tSums of self-adjoint operators ;$tAnother counterexample ;$gExercises --$tThe spectral theorem for unbounded self-adjoint operators:$tStatements of the spectral theorem ;$tStone's theorem and one-parameter unitary groups ;$tThe spectral theorem for bounded normal operators ;$tProof of the spectral theorem for unbounded self-adjoint operators ;$gExercises --$tThe harmonic oscillator:$tThe role of the harmonic oscillator ;$tThe algebraic approach ;$tThe analytic approach ;$tDomain conditions and completeness ;$gExercises --$tThe uncertainty principle:$tUncertainty principle, first version ;$tA counterexample ;$tUncertainty principle, second version ;$tMinimum uncertainty states ;$gExercises --$tQuantization schemes for Euclidean space:$tOrdering ambiguities ;$tSome common quantization schemes ;$tThe Weyl quantization for R²[superscript n] ;$tThe "No go" theorem of Groenewold ;$gExercises --$tThe Stone-Von Neumann theorem:$tA heuristic argument ;$tThe exponentiated commutation relations ;$tThe theorem ;$tThe Segal-Bargmann space ;$gExercises --$tThe WKB approximation:$gIntroduction ;$tThe old quantum theory and the Bohr-Sommerfeld condition ;$tClassical and semiclassical approximations ;$tThe WKB approximation away from the turning points ;$tThe Airy function and the connection formulas ;$tA rigorous error estimate ;$tOther approaches ;$gExercises --$tLie groups, Lie algebras, and representations:$gSummary ;$tMatrix Lie groups ;$tLie algebras ;$tThe matrix exponential ;$tThe Lie algebra of a matrix Lie group ;$tRelationships between Lie groups and Lie algebras ;$tFinite-dimensional representations of Lie groups and Lie algebras ;$tNew representations from old ;$tInfinite-dimensional unitary representations ;$gExercises --$tAngular momentum and spin:$tThe role of angular momentum in quantum mechanics ;$tThe angular momentum operators in R³ ;$tAngular momentum from the Lie algebra point of view ;$tThe irreducible representations of so(3) ;$tThe irreducible representations of SO(3) ;$tRealizing the representations inside L²(S²) --$tRealizing the representations inside L²(M³) ;$tSpin ;$tTensor products of representations : "addition of angular momentum" ;$tVectors and vector operators ;$gExercises --$tRadial potentials and the hydrogen atom:$tRadial potentials ;$tThe hydrogen atom : preliminaries ;$tThe bound states of the hydrogen atom ;$tThe Runge-Lenz vector in the quantum Kepler problem ;$tThe role of spin ;$tRunge-Lenz calculations ;$gExercises --$tSystems and subsystems, multiple particles:$gIntroduction ;$tTrace-class and Hilbert-Schmidt operators ;$tDensity matrices : the general notion of the state of a quantum system ;$tModified axioms for quantum mechanics ;$tComposite systems and the tensor product ;$tMultiple particles : bosons and fermions ;$t"Statistics" and the Pauli exclusion principle ;$gExercises --$tThe path integral formulation of quantum mechanics:$tTrotter product formula ;$tFormal derivation of the Feynman path integral ;$tThe imaginary-time calculation ;$tThe Wiener measure ;$tThe Feynman-Kac formula ;$tPath integrals in quantum field theory ;$gExercises --$tHamiltonian mechanics on manifolds:$tCalculus on manifolds ;$tMechanics on symplectic manifolds ;$gExercises --$tGeometric quantization on Euclidean space:$gIntroduction ;$tPrequantization ;$tProblems with prequantization ;$tQuantization ;$tQuantization of observables ;$gExercises --$tGeometric quantization on manifolds:$gIntroduction ;$tLine bundles and connections ;$tPrequantization ;$tPolarizations ;$tQuantization without half-forms ;$tQuantization with half-forms : the real case ;$tQuantization with half-forms : the complex case ;$tPairing maps ;$gExercises --$tA review of basic material:$tTensor products of vector spaces ;$tMeasure theory ;$tElementary functional analysis ;$tHilbert spaces and operators on them 650 0$aQuantum theory$xMathematics 830 0$aGraduate texts in mathematics ;$v267 907 $a.b14324635$b05-06-17$c30-05-17 912 $a991003377429707536 945 $aLE013 81-XX HAL11 (2013)$g1$i2013000294865$lle013$op$pE72.79$q-$rl$s- $t0$u2$v0$w2$x0$y.i15809547$z05-06-17 996 $aQuantum theory for mathematicians$9836756 997 $aUNISALENTO 998 $ale013$b30-05-17$cm$da $e-$feng$gnyu$h0$i0