A particle starts out (t=0) in the N-th state of the infinite square well. Now the "floor" of the well rises suddenly by an amount V0 (that is, H′=V0, for 0<x<a, and zero outside); after a time T the perturbation is removed.
(a) In first-order perturbation theory, what is the probability that the particle is now in the n-th state (in terms of n, N, V0, a, T, ℏ, and the energies En)? Note that there are actually two cases: n=N and n=N.
(b) Can this system make a transition to any other state? Explain.