Let ψ (x, t 0) / 3 + ψ2n4 + 3 (5/12), where vi is the ith normalized stationary state solution of the infinite square well (a) verify that v itself is normalized (b) find v (r, t) and using the explicit wavefunctions express the probability density at time t as a real function (c) if en is the energy of the nth normalized stationary state, what are the probabilities of measuring energy and getting the result eı, or e2, or ez? (d) what is < h > when written in terms of e1? (e) compute and < p>