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
/ (2
i
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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sep
2009