How to determine band structure (E(k)) of a one dimensional crystal?

[Wicked85]

Hi!
I'm new to the physics forum but I've read a little bit and I'm impressed with the knowledge a lot of people have here. I've tried searching for any topic on my question without any luck.

My question is simply what the algorithm is to determine the band structure for a one dimensional crystal (I'm supposed to do it by hand), this seems fairly easy but I just don't know where to start!

Any help would be GREATLY appreciated! :)
Thanks!
Simon

 

[Wicked85]

I should add that it's two atoms in the chrystal, A & B spaced a/2 units apart.

 

[kanato]

Are you doing tight-binding with one orbital per atom and only nearest neighbor hopping?

 

[Wicked85]

Yes, that's correct. Any ideas? :)