소장자료
LDR | 07885cam a2200409 i 4500 | ||
001 | 0092168950▲ | ||
003 | OCoLC▲ | ||
005 | 20180521075901▲ | ||
008 | 130224t20132013nyu b 001 0 eng c▲ | ||
016 | 7 | ▼a016488175▼2Uk▲ | |
020 | ▼a9781461471158▲ | ||
020 | ▼a146147115X▲ | ||
029 | 1 | ▼aCHVBK▼b220210918▲ | |
029 | 1 | ▼aAU@▼b000051751573▲ | |
035 | ▼a(OCoLC)828487961▲ | ||
040 | ▼aBTCTA▼beng▼erda▼cBTCTA▼dYDXCP▼dCSA▼dOHX▼dTXA▼dOCLCQ▼dUKMGB▼dSTF▼dHEBIS▲ | ||
082 | 0 | 4 | ▼a530.12▼221▲ |
090 | ▼a530.12▼bH174q▲ | ||
100 | 1 | ▼aHall, Brian C.,▼eauthor.▲ | |
245 | 1 | 0 | ▼aQuantum theory for mathematicians /▼cBrian C. Hall.▲ |
264 | 1 | ▼aNew York :▼bSpringer,▼c[2013]▲ | |
300 | ▼axvi, 554 pages ;▼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 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? --▼tSchro?dinger and heisenberg --▼tA matter of interpretation --▼tExercises --▼tA first approach to classical mechanics --▼tMotion in R1 --▼tMotion in Rn --▼tSystems of particles --▼tAngular momentum --▼tPoisson brackets and hamiltonian mechanics --▼tThe kepler problem and the runge-lenz vector --▼tExercises --▼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 Rn --▼tSystems of multiple particles --▼tPhysics notation --▼tExercises --▼tThe free schro?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 --▼tExercises --▼tParticle in a Square Well --▼tThe time-independent schro?dinger equation --▼tDomain questions and the matching conditions --▼tFinding square-integrable solutions --▼tTunneling and the classically forbidden region --▼tDiscrete and continuous spectrum --▼tExercises --▼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 --▼tExercises --▼tThe spectral theorem for bounded self-adjoint operators : proofs --▼tProof of the spectral theorem, first version --▼tProof of the spectral theorem, second version --▼tExercises --▼tUnbounded self-adjoint operators --▼tIntroduction --▼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 --▼tExercises --▼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 --▼tExercises --▼tThe harmonie oscillator --▼tThe role of the harmonie oscillator --▼tThe algebraic appfoach --▼tThe analytic approach --▼tDomain conditions and completeness --▼tExercises --▼tThe uncertainty principle --▼tUncertainty principle, first version --▼tA counterexample --▼tUncertainty principle, second version --▼tMinimum uncertainty states --▼tExercises --▼tQuantization schemes for euclidean space --▼tOrdering ambiguities --▼tSome common quantization schemes --▼tThe weyl quantization for R2n --▼tThe "No Go" theorem of groenewold --▼tExercises --▼tThe Stone-von Neumann Theorem --▼tA Heuristic argument --▼tThe exponentiated commutation relations --▼tThe theorem --▼tThe segal bargmann space --▼tExercises --▼tThe WKB approximation --▼tIntroduction --▼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 --▼tExercises --▼tLie groups, lie algebras, and representations --▼tSummary --▼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 --▼tExercises --▼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 --▼tExercises --▼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 --▼tExercises --▼tSystems and subsystems, multiple particles --▼tIntroduction --▼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 --▼tExercises --▼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 --▼tExercises --▼tHamiltonian mechanics on manifolds --▼tCalculus on manifolds --▼tMechanics on symplectic manifolds --▼tExercises --▼tGeometrie quantization on euclidean space --▼tIntroduction --▼tPrequantization --▼tProblems with prequantization --▼tQuantization --▼tQuantization of observables --▼tExercises --▼tGeometrie quantization on manifolds --▼tIntroduction --▼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 --▼tExercises --▼tA review of basic material --▼tTensor products of vector spaces --▼tMeasure theory --▼tElementary functional analysis --▼tHilbert spaces and operators on them --▼gReferences --▼gIndex.▲ |
650 | 0 | ▼aQuantum theory▼xMathematics.▲ | |
650 | 7 | ▼0(DE-588)4047989-4▼0(DE-603)085133809▼aQuantenmechanik▼2gnd▲ | |
650 | 7 | ▼0(DE-588)4155620-3▼0(DE-603)085662054▼aMathematische Methode▼2gnd▲ | |
830 | 0 | ▼aGraduate texts in mathematics ;▼v267.▲ | |
938 | ▼aBaker and Taylor▼bBTCP▼nBK0012854617▲ | ||
938 | ▼aOtto Harrassowitz▼bHARR▼nhar135015192▲ | ||
938 | ▼aYBP Library Services▼bYANK▼n10200195▲ | ||
994 | ▼aC0▼bUPK▲ | ||
999 | ▼c장화옥▲ |
Quantum theory for mathematicians
자료유형
국외단행본
서명/책임사항
Quantum theory for mathematicians / Brian C. Hall.
개인저자
형태사항
xvi, 554 pages ; 24 cm.
총서사항
서지주기
Includes bibliographical references and index.
내용주기
The experimental origins of quantum mechanics -- Is light a wave or a particle? -- Is an electron a wave or a particle? -- Schro?dinger and heisenberg -- A matter of interpretation -- Exercises -- A first approach to classical mechanics -- Motion in R1 -- Motion in Rn -- Systems of particles -- Angular momentum -- Poisson brackets and hamiltonian mechanics -- The kepler problem and the runge-lenz vector -- Exercises -- First approach to quantum mechanics -- Waves, particles, and probabilities -- A few words about operators and their adjoints -- Position and the Position Operator -- Momentum and the momentum operator -- The position and momentum operators -- Axioms of quantum mechanics : operators and measurements -- Time-evolution in quantum theory -- The heisenberg picture -- Example : a particle in a box -- Quantum mechanics for a particle in Rn -- Systems of multiple particles -- Physics notation -- Exercises -- The free schro?dinger equation -- Solution by means of the fourier transform -- Solution as a convolution -- Propagation of the wave packet : first approach -- Propagation of the wave packet : second approach -- Spread of the Wave Packet -- Exercises -- Particle in a Square Well -- The time-independent schro?dinger equation -- Domain questions and the matching conditions -- Finding square-integrable solutions -- Tunneling and the classically forbidden region -- Discrete and continuous spectrum -- Exercises -- Perspectives on the spectral theorem -- The difficulties with the infinite-dimensional case -- The goals of spectral theory -- A guide to reading -- The position operator -- Multiplication operators -- The momentum operator -- The spectral theorem for bounded self-adjoint operators : statements -- Elementary properties of bounded operators -- Spectral theorem for bounded self-adjoint operators, I -- Spectral theorem for bounded self-adjoint operators, II -- Exercises -- The spectral theorem for bounded self-adjoint operators : proofs -- Proof of the spectral theorem, first version -- Proof of the spectral theorem, second version -- Exercises -- Unbounded self-adjoint operators -- Introduction -- Adjoint and closure of an unbounded operator -- Elementary properties of adjoints and closed operators -- The spectrum of an unbounded operator -- Conditions for self-adjointness and essential self-adjointness -- A counterexample -- An example -- The basic operators of quantum mechanics -- Sums of self-adjoint operators -- Another counterexample -- Exercises -- The spectral theorem for unbounded self-adjoint operators -- Statements of the spectral theorem -- Stone's theorem and one-parameter unitary groups -- The spectral theorem for bounded normal operators -- Proof of the spectral theorem for unbounded self-adjoint operators -- Exercises -- The harmonie oscillator -- The role of the harmonie oscillator -- The algebraic appfoach -- The analytic approach -- Domain conditions and completeness -- Exercises -- The uncertainty principle -- Uncertainty principle, first version -- A counterexample -- Uncertainty principle, second version -- Minimum uncertainty states -- Exercises -- Quantization schemes for euclidean space -- Ordering ambiguities -- Some common quantization schemes -- The weyl quantization for R2n -- The "No Go" theorem of groenewold -- Exercises -- The Stone-von Neumann Theorem -- A Heuristic argument -- The exponentiated commutation relations -- The theorem -- The segal bargmann space -- Exercises -- The WKB approximation -- Introduction -- The old quantum theory and the bohr sommerfeld condition -- Classical and semiclassical approximations -- The WKB approximation away from the turning points -- The airy function and the connection formulas -- A rigorous error estimate -- Other approaches -- Exercises -- Lie groups, lie algebras, and representations -- Summary -- Matrix lie groups -- Lie algebras -- The matrix exponential -- The lie algebra of a matrix lie group -- Relationships between lie groups and lie algebras -- Finite-dimensional representations of lie groups and lie algebras -- New representations from old -- Infinite-dimensional unitary representations -- Exercises -- Angular momentum and spin -- The role of angular momentum in quantum mechanics -- The angular momentum operators in R3 -- Angular momentum from the lie algebra point of view -- The irreducible representations of so(3) -- The irreducible representations of SO(3) -- Realizing the representations inside L2(S2) -- Realizing the representations inside L2(M3) -- Spin -- Tensor products of representations : "addition of angular momentum" -- Vectors and vector operators -- Exercises -- Radial potentials and the hydrogen atom -- Radial potentials -- The hydrogen atom : preliminaries -- The bound states of the hydrogen atom -- The runge lenz vector in the quantum kepler problem -- The role of spin -- Runge-Lenz calculations -- Exercises -- Systems and subsystems, multiple particles -- Introduction -- Trace-class and hilbert-schmidt operators -- Density matrices: the general notion of the state of a quantum system -- Modified axioms for quantum mechanics -- Composite systems and the tensor product -- Multiple particles : bosons and fermions -- "Statistics" and the pauli exclusion principle -- Exercises -- The path integral formulation of quantum mechanics -- Trotter product formula -- Formal derivation of the feynman path integral -- The imaginary-time calculation -- The wiener measure -- The feynman-kac formula -- Path integrals in quantum field theory -- Exercises -- Hamiltonian mechanics on manifolds -- Calculus on manifolds -- Mechanics on symplectic manifolds -- Exercises -- Geometrie quantization on euclidean space -- Introduction -- Prequantization -- Problems with prequantization -- Quantization -- Quantization of observables -- Exercises -- Geometrie quantization on manifolds -- Introduction -- Line bundles and connections -- Prequantization -- Polarizations -- Quantization without half-forms -- Quantization with half-forms : the real case -- Quantization with half-forms : the complex case -- Pairing maps -- Exercises -- A review of basic material -- Tensor products of vector spaces -- Measure theory -- Elementary functional analysis -- Hilbert spaces and operators on them -- References -- Index.
ISBN
9781461471158 146147115X
청구기호
530.12 H174q
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