Time dependent wave function normalization

wolski888

1. The problem statement, all variables and given/known data
Below is a wave function that is a linear combination of 2 stationary states of the infinite square well potential. Where ψ1(x) and ψ2(x) are the normalized solution of the time independent Schrodinger equation for n=1 and n=2 states.

Show that the wave function is properly normalized.
2. Relevant equations

1 = Integral (-inf, inf) of [itex]\Psi[/itex][itex]\Psi[/itex]* dx

3. The attempt at a solution

When I tried solving the integral I can't seem to get any where. The fact that the wave function has 2 terms being added to each other complicates things. I looked at my textbook for help but the examples show only for time independent wave functions with one term. And tips and hints on how to approach this problem?

Thanks for reading this post.

hexiphysics

Think about what you know about solutions to the time independent Schrodinger equation. What does integral (-inf, inf) Psi1(x)^2 equal? What do you know about integrating stationary states of different energy levels from (-inf, inf). Hope this helps!

(sorry I don't know how to make the equations and variables look nice, first time posting)