I think I see what you are saying. I will give a little more information into what I am trying to do.
The question is:
Consider two normalizable wave functions Ψ1(x, t) and Ψ2(x, t), both of which are solutions
of the time-dependent Schrodinger equation. Assume that the potential function is real.
The functions are normalized, and the functions both approach zero as x goes to ±∞.
Show that these propeties can be used to prove that
\frac{d}{dt} \int_{-∞}^{∞} Ψ1*(x, t)Ψ2(x, t)dx = 0
We get a hint to conert the temporal derivative to the spatial dertivative using the time-dependent schrodinger equation and you get:
\frac{i\bar{h}}{2m} \int_{-∞}^{∞} Ψ1*(x, t)\frac{d^2}{dx^2}Ψ2(x, t) - Ψ2(x, t)\frac{d^2}{dx^2}Ψ1*(x, t)
Then using integration by parts you entually get a term (for one part of the integral) that is
Ψ1*(x, t)\frac{d}{dx}Ψ2(x, t) |^{∞}_{-∞}
and I need that to go to 0 or else the rest doesn't really follow through correctly. I justified it by saying that since Ψ2(x, t) goes to 0 and +- infinity then its derivative will go to 0 and +- infinity.
