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Exact Solution of an Isotonic Oscillator with a Time Dependant Hamitonian

Zhang Jie

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

We present the exactsolution of the Schr dinger equation of an oscillator with mass,frequency and centripetal barrierall vorying with time though a canonical transformation and give a correct representation for the ground state energy.

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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.