Problem 1. A particle of mass m, which moves freely inside an infinite potential well of length a, has the following initial wave function at t = 0: A (x, 0) = sin να sin (17) + 3 -sin 5a n(377). 1 + sin √5a in (57) a (a) Find A so that (x, 0) is normalized. (b) If measurements of the energy are carried out, what are the values that will be found and what are the corresponding probabilities? Calculate the average energy. (c) Find the wavefunction (x, t) at any later time t. (d) Determine the probability of finding the system at a time to in the state p(x,t) = e-Esto/h; then determine the probability of finding the system in the state sin() e Φ (x, to) = √²sin (2x) e-lEzto/h