Show that
[frac{d}{dt}int_{-infty}^{infty} Psi_{1}^{*}Psi_{2}dx = 0]
for any two normalizable solutions to the Schrödinger equation, (Psi_{1}) and (Psi_{2}), for the same potential (V(x)). Why wouldn't this be true if they were solutions for different potentials? (Hint: For the proof, integration by parts may come in handy. For the second part, you shouldn't have to do any more math, just point to the part in your proof that would change.)