Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

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Time-dependent propagator for an-harmonic oscillator with quartic term in potential

Journal of Mathematical Physics ◽

10.1063/5.0018545 ◽

2021 ◽

Vol 62 (2) ◽

pp. 023501

Author(s):

J. Boháčik ◽

P. Prešnajder ◽

P. Augustín

Keyword(s):

Harmonic Oscillator ◽

Time Dependent ◽

Quartic Term

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Transition probabilities of harmonic oscillator system with spatial Linear-Quadratic-Cubic (LQC) perturbation in time-dependent

Journal of Physics Conference Series ◽

10.1088/1742-6596/1918/2/022025 ◽

2021 ◽

Vol 1918 (2) ◽

pp. 022025

Author(s):

Herry F. Lalus ◽

N P Aryani

Keyword(s):

Harmonic Oscillator ◽

Transition Probabilities ◽

Time Dependent ◽

Linear Quadratic ◽

Oscillator System

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GENERALIZED HANNAY ANGLE FOR THE MOST GENERAL TIME-DEPENDENT HARMONIC OSCILLATOR

International Journal of Modern Physics B ◽

10.1142/s0217979293003851 ◽

1993 ◽

Vol 07 (28) ◽

pp. 4827-4840 ◽

Cited By ~ 2

Author(s):

DONALD H. KOBE ◽

JIONGMING ZHU

Keyword(s):

Harmonic Oscillator ◽

Berry Phase ◽

Time Dependent ◽

Canonical Momentum ◽

Gauge Invariant ◽

Classical Counterpart ◽

Mass Spring ◽

Adiabatic Case ◽

General Time ◽

Total Angle

The most general time-dependent Hamiltonian for a harmonic oscillator is both linear and quadratic in the coordinate and the canonical momentum. It describes in general a harmonic oscillator with mass, spring “constant,” and friction (or antifriction) “constant,” all of which are time dependent, that is acted on by a time-dependent force. A generalized Hannay angle, which is gauge invariant, is defined by making a distinction between the Hamiltonian and the energy. The generalized Hannay angle is the classical counterpart of the generalized Berry phase in quantum theory. When friction is present the generalized Hannay angle is nonzero. If the Hamiltonian is (incorrectly) chosen to be the energy, the generalized Hannay angle is different. Nevertheless, in the adiabatic case the same total angle is obtained.

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