Quantum Oscillators  

Quantum Harmonic Oscillator > s.a. feynman propagator; formulations [combinatorial]; oscillators; time in quantum theory.
* Propagator: The Feynman propagator for the quantum harmonic oscillator is (t:= t2–t1)

DF(x2, t2; x1, t1) = [m / (2i sin(t))1/2] exp{i m/2 [(x22+x12) · (t) – 2 x2x1 csc(t)] } .

@ General references: Jauch & Hill PR(40); Leubner et al AJP(88)dec [vs classical]; Boya et al IJMPA(98) [inequivalent]; Muñoz AJP(98)mar [and integral equations]; Jordan AJP(01)oct [simple solution]; Baker et al AJP(02)may [applications, numerical]; Kastrup AdP(07)qp/06 [new look]; Plimak & Stenholm AP(08) [response properties]; Marsiglio AJP(09)mar [and bound states of short-range potentials].
@ 2D: Chen & Huang JPA(03) [coherent states, vortex structure]; Montesinos & Torres del Castillo PRA(04), comment Latimer PRA(07)qp/06 [different symplectic structures]; Doll & Ingold AJP(07)mar [semiclassical, Lissajous curves].
@ Entanglement: Kim & Iafrate FPL(04) [coupled]; Rios JPA(07) [non-interacting]; Jost et al Nat-a0901 [non-interacting, demonstration].
@ Coupled oscillators: Maxson ht/03, ht/03, ht/03, ht/03 [correlated]; Colosi a0706 [general relativistic, two-point function].
@ Coupled to heat bath: Ford & O'Connell PhyE(05)qp/06; Isar & Scheid PhyA(07)-a0705 [decoherence and classical correlations].
@ Different quantizations: Donoghue & Holstein AJP(88)mar [path integral]; Koikawa PTP(01)ht, PTP(02)ht/01 [Moyal]; Shiri-Garakani & Finkelstein JMP(06) [general quantization]; Finkelstein & Shiri-Garakani qp/06 [as model for spacetime decondensation]; Nettel & Quevedo mp/06-in [topological quantization]; Vicary IJTP(08) [categorical framework]; > s.a. path integrals [non-standard].
@ Green function: Khrebtukov & Macek JPA(98); > s.a. feynman propagator.
@ Related topics: de la Peña & Cetto JMP(79) [and stochastic electrodynamics]; Dattoli & Torre NCB(95) [phase space, coherent states]; Lorente PLA(01)qp/04 [discrete model]; Morigi et al PRA(02) [irreversibility]; Leshem & Gat PRL(09) [violation of macroscopic realism].
> States: see fock space; coherent states; hilbert space [inverted]; representations of quantum mechanics [Bargmann].
> Other topics: see approaches to quantum mechanics; deformation quantization; geometric quantization; quantum-classical coupling; resonance.

Damped Oscillator > s.a. quantum probability.
* Idea: A dissipative system; > s.a. dissipation.
@ General references: Pedrosa & Baseia PRD(84) [+ oscillator bath]; Milburn & Holmes PRL(96); Isar & Sandulescu RJP(92)qp/06 [rev]; de Brito et al NCB(98); Um et al PRP(02); Banerjee & Mukherjee JPA(02)qp/01 [canonical approach]; Blasone et al qp/03-in; Montesinos PRA(03) [Heisenberg picture]; Latimer JPA(05)qp/04; López & López qp/05; Endo et al IJGMP(08)-a0710, Fujii & Suzuki IJGMP(09)-a0806 [general solution]; Cordero-Soto et al a0905.
@ Related topics: Kheirandish & Amooshahi MPLA(05)qp [radiation reaction]; Chruscinski & Jurkowski AP(06) [resonances]; Isar O&S(07)qp/06-in [decoherence, Lindblad theory].
@ In alternative approaches: Vandyck JPA(94) [pilot-wave theory]; Dito & Turrubiates PLA(06)qp/05 [deformation quantization]; Fujii qp/07-in [complex time]; Streklas PhyA(07) [on non-commutative plane]; > s.a. wigner functions.

Other Types and Effects > s.a. decoherence; histories formulation; Perturbation Methods.
@ Relativistic: Guerrero & Aldaya MPLA(99) [perturbative]; Toyama & Nogami PRA(99); Bars a0810.
@ Bateman's dual system: (A damped simple harmonic oscillator coupled to its time-reversed image) Blasone & Jizba AP(04)qp/01.
@ Inverted: Blume-Kohout & Zurek PRA(03)qp/02 [upside down, decoherence]; Chruscinski JMP(04)mp/03; Yuce et al PS(06).
@ Quartic: Pesquera & Claverie JMP(82) [in stochastic electrodynamics]; Matamala & Maldonado PLA(03), Liverts et al JMP(06) [spectrum and eigenfunctions, analytic].
@ Anharmonic / non-linear / perturbed: Pathak JPA(00)mp/02; Speliotopoulos JPA(00) [spectrum]; Calogero & Graffi PLA(03); Calogero PLA(03); Gómez & Sesma qp/04-in [bound states], JPA(05)qp [new approach]; Matzkin & Lombardi JPA(05)-a0706 [quantum and semiclassical phase functions]; Cariñena et al AP(07) [solvable]; Liverts & Mandelzweig PS(08) [approximate solution]; Fernández a0804 [eigenvalues, upper and lower bounds]; Midya & Roy JPA(09) [exactly solvable, quasi-exactly solvable et al]; Wang & Liu IJTP(09); > s.a. coherent states.
@ Anharmonic, perturbation methods: Cicuta ht/97; Amore mp/04-in [classical and quantum]; Voros mp/06-in; > s.a. Perturbation.
@ On the sphere and hyperbolic space: Cariñena et al AP(07)-a0709 [2D]; Mardoyan a0708-in [in d dimensions].
@ Dirac oscillator: Martínez-y-Romero et al EJP(95)qp/99; Alhaidari IJTP(04)ht [Green function]; > s.a. green function.
@ Forced, time-dependent: Dodonov PLA(96) [kicked]; Graffi & Yajima mp/00 [forced]; Kim & Yee PRA(02)ht; Moya-Cessa & Fernández-Guasti PLA(03)qp [sudden change, coherent states]; Adler JPA(05)qp/04 [stochastic collapse and decoherence]; Gómez & Villaseñor AP(09) [and quantum field theory]; > s.a. stochastic quantization.
@ Deformed: Man'ko et al qp/97-in; De Freitas & Salamó ht/99; Gruver PLA(99); Sogami & Koizumi mp/01; Isar & Scheid PhyA(02)qp/07, PhyA(04)qp/07 [in dissipative environment]; Albanese & Lawi JPA(04)ht/03; Narayana Swami qp/04 [and intermediate statistics]; Jafarov et al JPA(07)mp [Wigner function]; > s.a. modified coherent states [including Grassmann].
@ With gup: Chang et al PRD(02)ht/01; Nouicer PLA(06); Gemba et al a0712 [algebraic solution, deformed su(1,1) algebra]; Fakel & Merad JMP(09).
@ Pais-Uhlenbeck oscillator: (An example of higher-derivative theory) Mannheim & Davidson PRA(05)ht/04 [Dirac quantization]; Andrzejewski et al a0904 [Euclidean path-integral approach].
@ Other types: Dragovich TMP(94)ht/04, IJMPA(95)ht/04 [adelic]; Thienel JPA(96) [supersymmetric, Bargmann representation]; Banerjee & Ghosh JPA(98) [chiral]; Badescu & Landsberg JPA(02) [-oscillator]; Kim & Page qp/02 [generalized]; Blasone et al PLA(03)qp/02 [group contraction]; Bhattacharyya & Bhattacharjee PLA(04) [subharmonic, V |x|r]; > s.a. stochastic quantization [Fermi oscillator].

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