Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9605046 · Physical Review A

Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator

Hyeong-Chan Kim, Minho Lee, Jeong‐Young Ji, Jae Kwan Kim

Published Jun 1, 1996• 44 citations
arXivHTMLPDF

Abstract

In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to two interesting cases. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.3767

Related papers

Heisenberg-picture approach to the exact quantum motion of a time-dependent harmonic oscillator

Jeong‐Young Ji, Jae Kwan Kim, Sang Pyo Kim

The generalized invariant and the exact quantum motions are found in the Heisenberg picture for a harmonic oscillator with time-dependent mass and frequency in terms of classical solutions. It is shown that the Heisenberg pictures gives a relatively simpler picture that the Schr\"odinger picture and also manifestly exhibits the time independency of the invariant. We apply this method to the system with a linear sweep of frequency and Paul trap and study the squeezing properties.

Physical Review A•May 1, 1995•114 citations

Heisenberg picture approach to the invariants and the exact quantum motions for coupled parametric oscillators

Jeong-Young Ji, Jongbae Hong

For N -coupled generalized time-dependent oscillators, primary invariants and a generalized invariant are found in terms of classical solutions. Exact quantum motions satisfying the Heisenberg equation of motion are also found. For number states and coherent states of the generalized invariant, the uncertainties in positions and momenta are obtained.

arXiv:quant-ph/9808003•Journal of Physics A Mathematical and General•Oct 2, 1998•10 citations

Forced harmonic oscillator in the interaction picture

Richard A. Ferrell

The interaction picture of quantum mechanics is used to calculate the unitary time development operator for a harmonic oscillator subject to an arbitrary time-dependent force. The result is identical to that obtained from the more usual method of the Heisenberg equations of motion, except for a phase factor which the Heisenberg picture method is unable to determine. A simplified derivation of the phase factor is given in the adiabatic limit, as well as a discussion of some possible physical effects which would depend upon the phase factor.

American Journal of Physics•May 1, 1977•18 citations

Time-dependent harmonic oscillator with variable mass under the action of a driving force

M. Sebawe Abdalla

An exact solution is presented for the problem of a harmonic oscillator of time-dependent mass with an external driving force. The wave functions for both pseudostationary and quasicoherent states and the Green's function are calculated. A solution is obtained in the Heisenberg picture. The amplitude for transition from a coherent state to a simple harmonic-oscillator coherent state is calculated.

Physical Review A•Dec 1, 1986•53 citations

Exact wave functions and coherent states of a damped driven harmonic oscillator

H. G. Oh, H. R. Lee, Thomas F. George +1 more

For a damped harmonic oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) path integral, (ii) second quantization, and (iii) dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, overcomplete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator.

Physical Review A•Jun 1, 1989•40 citations

Forced Time-Dependent Harmonic Oscillators in Non-Commutative Space

Mai-Lin Liang

For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis—Riesenfeld invariant. Coherent states are obtained as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.

Communications in Theoretical Physics•Mar 1, 2011•2 citations
In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to two interesting cases. \textcopyright{} 1996 The American Physical Society.
The interaction picture of quantum mechanics is used to calculate the unitary time development operator for a harmonic oscillator subject to an arbitrary time-dependent force. The result is identical to that obtained from the more usual method of the Heisenberg equations of motion, except for a phase factor which the Heisenberg picture method is unable to determine. A simplified derivation of the phase factor is given in the adiabatic limit, as well as a discussion of some possible physical effects which would depend upon the phase factor.
For a damped harmonic oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) path integral, (ii) second quantization, and (iii) dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, overcomplete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator.