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Journal of Hunan University

Double Wave Description of Time dependent Harmonic Oscillator

Zhu Zheng

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

A harmonic oscillator with time dependent frequancy is studied using double wave function theory.The calculation of displacement,momentum and energy etc,shows that the oscillator moves quasi harmonically in time.When the frequancy comes to a constant,the oscillator becomes the simple harmonic one,as expected.

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The time-dependent Schrdinger equation for the harmonic oscillator with time-dependent frequency ω=ω(t) and mass m=m(0)ω(0)ω(t)exp[2c∫t0ω(t)dt] can be solved by means of simple transformation and separation of variables.The wave functions are obtained for c21,c2=1 and c21,respectively.When |x|→∞,the wave function for c21 tends to zero but it is not so for c2≥1.Finally,some special cases are given for the time-dependent harmonic oscillator and one of them is similar to a damped harmonic oscillator.