Question

1. A particle, initially (t -> 0) in the ground state of an infinite, 1D potential box with walls at r 0 and = a, is subjected at time t = 0 to a time-dependent perturbation V (r, t) et/7, with eo a small real number a) Calculate to first order the probability of finding the particle in an excited state for t 0. Consider all final states. Are all possible transitions allowed? b) Examine the time dependence of the problem: Make a sketch and describe with words the behavior of the transition probability as a function of time induced by the perturbation c) Calculate the probability that, after a sufficiently long time, the system will have made such a transition (i.e., analyze the limit t -> 00) d) How would the previous results you found in a)-c) change if the particle starts from the ground state in a 1D harmonic oscillator potential? Be specific and justify your answers appropriately

Answer 1

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