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Journal of Physics A Mathematical and General

Harmonic oscillator with strongly pulsating mass

R. K. Colegrave, M. Sebawe Abdalla

Published May 1, 1982• 64 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/15/5/016

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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.
In this paper, the propagator for a harmonic oscillator with mass obeying the function of m(t)=mtan2νt is derived by the Feynman path integral method. The wave function of this oscillator is calculated by expanding the obtained propagator. The propagator for a harmonic oscillator with strongly pulsating mass is evaluated by the Schwinger method. The propagator for a harmonic oscillator with mass rapidly growing with time is calculated by applying the integrals of the motion of quantum systems. The comparison between these methods are also discussed.
The exact solutions to the time-dependent Schrodinger equation for a harmonic oscillator with time-dependent mass and frequency were derived in a general form. The quantum mechanical propagator was calculated by the Feynman path integral method, while the wave function was derived from the spectral representation of the obtained propagator. It was shown that the propagator and the wave function depended on the s solution of a classical oscillator, in which the amplitude and phase satisfied the auxiliary equations. To demonstrate the derivation of the solution from our auxiliary equations, exponential and periodic functions of mass with constant frequency were imposed to evaluate the propagator and wave function for the Caldirola-Kanai and pulsating mass oscillators, respectively.