Question: Consider a particle bound in a simple harmonic-oscillator potential. Initially (t < 0), it is in the ground state. At t = 0 a perturbation

Consider a particle bound in a simple harmonic-oscillator potential. Initially (t < 0), it is in the ground state. At t = 0 a perturbation of the form

is switched on. Using time-dependent perturbation theory, calculate the probability that after a sufficiently long time (t ≫ τ), the system will have made a transition to a given excited state. Consider all final states.

H'(x,t) = Axe-t/t

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