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

Physical Review A

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

M. Sebawe Abdalla

Published Dec 1, 1986• 53 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.34.4598

Related papers

Canonical treatment of harmonic oscillator with variable mass

M. Sebawe Abdalla

By the use of a canonical transformation the problem of the harmonic oscillator with a time-dependent mass has been transformed to that of an oscillator with a time-dependent frequency. Pseudostationary and quasicoherent states are discussed.

Physical Review A•May 1, 1986•66 citations

The quantum mechanical linearly damped forced oscillator

Leon F. Landovitz, Alfred M. Levine, E. Ozizmir +1 more

The solution is obtained to the quantum mechanical linearly damped harmonic oscillator subjected to a time dependent driving force. This solution allows the calculation of interesting quantum quantities such as the Green’s function and the transition amplitudes between harmonic oscillator states. The specific results for a harmonic driving force are given.

The Journal of Chemical Physics•May 15, 1983•7 citations

Harmonic oscillator with strongly pulsating mass

R. K. Colegrave, M. Sebawe Abdalla

An exact solution is presented for the problem of a harmonic oscillator of frequency ω 0 and mass varying with time according to M = M O cos 2 νt. The solution is closely related to that of an oscillator of constant mass M O and frequency (ω O 2 + ν 2 ) 1/2 . Pseudostationary and quasicoherent states are discussed. Applications in quantum optics are foreseen.

Journal of Physics A Mathematical and General•May 1, 1982•64 citations

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

Hyeong-Chan Kim, Minho Lee, Jeong‐Young Ji +1 more

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.

arXiv:quant-ph/9605046•Physical Review A•Jun 1, 1996•44 citations

Squeezed States of the Time-dependent Harmonic Oscillator Under the Action of an Arbitrary Driving Force

YU You-hong

By making use of the basic invariant, the squeezed states of the harmonic oscillator with a time-dependent mass under the action of an arbitrary driving force are constructed. The general of the invariants for the system is also obtained.

Acta Sinica Quantum Optica•Jan 1, 2001•0 citations

Unitary relations in time-dependent harmonic oscillators

Dae-Yup Song

For a harmonic oscillator with time-dependent (positive) mass and frequency, a unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as well as operators. For a driven harmonic oscillator, a unitary transformation which relates the driven system and a system of the same mass and frequency without a driving force is given, as a generalization of previous results, in terms of the solution of classical equation of motion of the driven system. Thus transformations give a simple way of finding exact wavefunctions of a driven harmonic oscillator system, provided the quantum states of the corresponding system of unit mass are given.

arXiv:quant-ph/9812038•Journal of Physics A Mathematical and General•Jan 1, 1999•24 citations
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.
For a harmonic oscillator with time-dependent (positive) mass and frequency, a unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as well as operators. For a driven harmonic oscillator, a unitary transformation which relates the driven system and a system of the same mass and frequency without a driving force is given, as a generalization of previous results, in terms of the solution of classical equation of motion of the driven system. Thus transformations give a simple way of finding exact wavefunctions of a driven harmonic oscillator system, provided the quantum states of the corresponding system of unit mass are given.