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 LEADER 02353nam 2200541z- 450 001 9910557377303321 005 20211118 035 $a(CKB)5400000000042117 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/72940 035 $a(oapen)doab72940 035 $a(EXLCZ)995400000000042117 100 $a20202111d2019 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aNeurocardiovascular Diseases: New Aspects of the Old Issues 210 $cFrontiers Media SA$d2019 215 $a1 online resource (155 p.) 225 1 $aFrontiers Research Topics 311 08$a2-88945-775-3 330 $aThis eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact 517 $aNeurocardiovascular Diseases 606 $aNeurosciences$2bicssc 606 $aScience: general issues$2bicssc 610 $aAtrial Fibrillation 610 $aAutonomic Nervous System 610 $aCerebral Blood Flow 610 $aGeneralized Poincare Plot 610 $aHeart Failure 610 $ainformation spectrum method 610 $amultiple trigonometric regressive spectral analysis 610 $aneurocardiovascular 610 $aObesity 610 $astress 615 7$aNeurosciences 615 7$aScience: general issues 700 $aBoji?$b Tijana$4edt$01296988 702 $aEsquinas$b Antonio M$4edt 702 $aFrancis Antonios$b Tarek$4edt 702 $aBoji?$b Tijana$4oth 702 $aEsquinas$b Antonio M$4oth 702 $aFrancis Antonios$b Tarek$4oth 906 $aBOOK 912 $a9910557377303321 996 $aNeurocardiovascular Diseases: New Aspects of the Old Issues$93024365 997 $aUNINA