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003			BD-DhAAL
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008			130405t20132013nyua b 001 0 eng c
010			_a 2013937175
016	7		_a016488175 _2Uk
020			_a9781461471158 (acidfree paper)
020			_a146147115X (acidfree paper)
020			_a9781461471165
035			_a(OCoLC)ocn828487961
040			_aBTCTA _beng _cBTCTA _erda _dYDXCP _dCSA _dOHX _dTXA _dOCLCQ _dUKMGB _dSTF _dHEBIS _dIQU _dPUL _dOCLCF _dIXA _dDLC _dBD-DhAAL
042			_apcc
050	0	0	_aQC174.12 _b.H346 2013
072		7	_aQA _2lcco
082			_a530.12 _222
100	1		_aHall, Brian C., _eauthor. _921848
245	1	0	_aQuantum theory for mathematicians / _cBrian C. Hall.
260			_aNew York : _bSpringer, _c2013.
300			_axvi, 554 pages : _billustrations ; _c24 cm
490	1		_aGraduate texts in mathematics, _x0072-5285 ; _v267
504			_aIncludes bibliographical references (pages 545-548) and index.
505	0	0	_tThe experimental origins of quantum mechanics: _tIs light a wave or a particle? ; _tIs an electron a wave or a particle? ; _tSchrödinger 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 Schrödinger 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 Schrödinger 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.
526			_aCSE
650		0	_aQuantum theory _xMathematics. _939415
650		0	_aQuantum theory.
650		0	_aMathematical physics.
650		0	_aComputer science.
830		0	_aGraduate texts in mathematics, _x0072-5285 ; _v267.
942			_2ddc _cBK
999			_c47003 _d47003