Sinusoidal Potential in Schroedinger

[Sturk200]

Hello,

How do you solve Schroedinger's equation (time-independent, in one dimension) if the potential is V=sin(x)? Do you have to use the series approximation for sin(x) and obtain a series solution for psi? Is there some way to use Bloch's theorem since the potential is periodic? I've only seen Bloch used for a periodic delta function potential. Does anybody know what these wave functions look like?

Thanks!

 

[blue_leaf77]

Is there some way to use Bloch's theorem since the potential is periodic?

Bloch theorem should be usable as it is derived for general periodic potentials. Reference wise, I think you might want to look at https://vcq.quantum.at/fileadmin/Publications/1999-12.pdf.