A particle is in the infinite square well of width a. Its initial wave function at time t = 0 is

(4 points) A particle is in the infinite square well of width a. Its initial wave function at time t = 0 is V(r, t = 0) = A 27/1 + ein/21/2 where v1, 12 are normalized and orthogonal cigenfunctions corresponding to energies E1, E2. (a) Normalize the wave function and find A. (b) Find I(x, t) and p = [I(x, t) |2. Write them in terms of explicit expressions for the infinite potential well. (c) Calculate the expectation value of the position operator in state V(x, t). Docs it depend on time? (d) Calculate the expectation value of the momentum operator in state V(r, t). You can use Ehrenfest theorem to do this. Does this expectation value depend on time? (e) What is expectation value of the Hamiltonian in state V? How does it compare with energies E1 and E2 ? (f) If you measured the energy, what values you can get and with what probabilities