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College Physics

The exact solution of the transition probability of a harmonic oscillator under time-dependent external uniform field

Bing Yuan

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

The exact wave functions of a time-dependent driven harmonic oscillator are obtained by the trial function method and the exact transition probability are calculated.

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Transition amplitudes and probabilities for the harmonic oscillator with a forcing function proportional to cos(ωt) beginning at time zero are calculated to lowest nonvanishing order using time-dependent perturbation theory. The results are compared with the exact amplitudes and probabilities. When the exact amplitude is expanded in a Taylor series in powers of the coupling constant, the individual terms turn out to be the perturbation amplitudes, showing that the complete series of perturbation amplitudes converges to the exact amplitude.