equation

topsquark

Forum Staff
Apr 2008
2,968
628
On the dance floor, baby!
in attachment
Just so we don't all have to download the file the question is

If
\(\displaystyle \psi (x) = \sum_{q}a_q e^{i q x}\)

Then does the Schrodinger equation become:
\(\displaystyle \sum_{q'} \left ( \dfrac{\hbar ^2 q'^2}{2m} e^{i q' x} + U e^{i (q' + g) x} + U e^{i (q' - g) x} \right ) a_{q'} = E \sum_{q} a_{q'} e^{i q' x}\)

A few points. Why are you using q' instead of just q? Where did the g come from? And finally I'm presuming your potential energy function is U(x) but I can't see how you would have got that form. It should be
\(\displaystyle U \psi = U ~ \sum_{q'} a_{q'} e^{i q' x}\)

-Dan
 
Oct 2017
561
282
Glasgow
I think it's just a case of substituting the wave function and processing it with the operators. Have you given it a go?