1) Problem 8.1 from Griffiths.
2) An electron is in the ground state of a harmonic potential well (V(x)= (1/2) mw2x2). If a pulse of electric field of the form E(t) = E0 exp(-(t/T)2), where E0 and T are constants, is applied in the x-direction starting at t = -infinity, using the first-order time-dependent perturbation theory,
(a) Calculate the probability that the particle will be found in the first excited state in the infinite time limit.
(b) Calculate the probability that the particle will be found in the second excited state in the infinite time limit; You do not have to do any integration for this part; Check the matrix element!