Time dependent wave function normalization

[wolski888]

Homework Statement

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 Schrödinger equation for n=1 and n=2 states.

Show that the wave function is properly normalized.

Homework Equations

1 = Integral (-inf, inf) of $\Psi$$\Psi$* dx

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 Schrödinger 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)