(i) Calculate, in the lowest nonvanishing order of the perturbation theory, the probability that the pulse drives the oscillator into its lowest excited state.
(ii) Compare the result with the exact solution of the problem.
(iii) Spell out the perturbative result for a Gaussian-shaped waveform,
F(t)=F0exp{−t2/τ2}
and analyze its dependence on the time scale τ of the pulse.