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

Canonical treatment of harmonic oscillator with variable mass

M. Sebawe Abdalla

Published May 1, 1986• 66 citations
Publisher

Abstract

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.
DOI
10.1103/physreva.33.2870

Related papers

Harmonic oscillator with time-dependent mass and frequency and a perturbative potential

CELIA M. A. DANTAS, I. A. Pedrosa, B. Baseia

A general treatment of the quantized harmonic oscillator with time-dependent mass and frequency is presented. The treatment is also applied to the time-dependent oscillator under the action of a time-dependent perturbative potential. The treatment is based on the use of some time-dependent transformations and in the method of invariants of Lewis and Riesenfeld [J. Math. Phys. 10, 1458 (1969)]. Exact coherent states for such systems are also constructed.

Physical Review A•Feb 1, 1992•107 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

A Novel Method to Solve the Exact Wave Function of Time-dependent Damped Harmonic Oscillator with Variable Mass

Rui Ling

Using the canonical transformation and the trial function method,the exact wave function of a time-dependent damped harmonic oscillator with variable mass is derived.

Journal of Changshu Institute of Technology•Jan 1, 2011•0 citations

Canonical Transformations for Time-Dependent Harmonic Oscillators

Tae Jun Park

A canonical transformation changes variables such as coordinates and momenta to new variables preserving either the Poisson bracket or the commutation relations depending on whether the problem is classical or quantal respectively. Classically canonical transformations are well established as a powerful tool for solving differential equations. Quantum canonical transformations have been defined and used relatively recently because of the non-commutativeness of the quantum variables. Three elementary canonical transformations and their composite transformations have quantum implementations. Quantum canonical transformations have been mostly used in time-independent Schrodinger equations and a harmonic oscillator with time-dependent angular frequency is probably the only time-dependent problem solved by these transformations. In this work, we apply quantum canonical transformations to a harmonic oscillator in which both angular frequency and equilibrium position are time-dependent.

Bulletin of the Korean Chemical Society•Feb 20, 2004•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

Quantum Mechanical Path Integral in Phase Space and Class of Harmonic Oscillators with Varied Frequencies

Badri Berrabah

We present the problem of the time-dependent Harmonic oscillator with time-dependent mass and frequency in phase space and by using a canonical transformation and delta functional integration we could find the propagator related to the system. New examples of time-dependent frequencies are presented.

Journal of Modern Physics•Jan 1, 2016•2 citations
A canonical transformation changes variables such as coordinates and momenta to new variables preserving either the Poisson bracket or the commutation relations depending on whether the problem is classical or quantal respectively. Classically canonical transformations are well established as a powerful tool for solving differential equations. Quantum canonical transformations have been defined and used relatively recently because of the non-commutativeness of the quantum variables. Three elementary canonical transformations and their composite transformations have quantum implementations. Quantum canonical transformations have been mostly used in time-independent Schrodinger equations and a harmonic oscillator with time-dependent angular frequency is probably the only time-dependent problem solved by these transformations. In this work, we apply quantum canonical transformations to a harmonic oscillator in which both angular frequency and equilibrium position are time-dependent.