An electron in an infinitely deep potential well of thickness 4 angstroms is placed in a linear superposition of the first and third states. What is the frequency of oscillation of the electron probability density?
The Attempt at a Solution
My main problem right now is with the normalization of the wave function:
I have ψTotal=Aψ1+ Bψ3
∫|ψT|^2=1=∫(|A|^2*sin^2(pi*z/Lz) +|B|^2*sin^2(3pi*z/Lz))dz (the other terms with A*B and B*A become zero after integration)
What I'd like to do next is calculate the probability density of the electrons, but I end up with |A|^2, |B|^2, A*B, & B*A terms and don't know how to get actual numbers for all these constants, or otherwise to properly normalize this. I know what to do if the superposition of states was equally split, but it does not say that here.
Any thoughts on what I'm doing wrong? Thanks