1. Separation of variables: In the lectures, we found general solutions to the Schrodinger equation using the approach of separa- tion of variables. Now, suppose you add a constant V0 to the potential energy of a system. In classical mechanics this doesn't change anything, but what about quantum mechanics? (a) Show that the wave functions satisfying the Schrodinger equation pick up a time-dependent phase factor: e'th/h. (b) What effect does this have on the expectation value of an observable calculated with these wave functions