Tight binding model, help please

[jiimmy1]

Homework Statement

In the tight binding model, (E=Eo + alpha + (2gamma coska)), how are parameters alpha and gamma affected if the lattice spacing, a, is increased?

I know the equations for gamma and alpha but can't type them in here because they involve integrals and I don't know how to put those in on this forum.

Thanks in advance!


Sorry, didn't realize how the forums worked, so posted in this area instead. Its taking far too long to figure out how to post the equations in latex on here so i apologise but this isn't technically homework help. My final year solid state physics 2 exam is tomorrow and this wasn't in our notes but is in the revision questions handed out so please don't delete this one!

 

[NateD]

Homework EquationsGamma = (2t/h-bar)int(0 to 1) dr r*sin(k_r*a)Alpha = -2t/h-bar int(0 to 1) dr r*cos(k_r*a)The Attempt at a SolutionI think gamma will increase and alpha will decrease as the lattice spacing increases. I think this because if a increases, the integral for gamma will be greater due to the higher values of both sin(k_r*a) and r*, and the integral for alpha will be smaller for the same reason. I'm more interested in why this is the case than just the answer though. Can someone explain why increasing the lattice spacing affects gamma and alpha the way it does? Thanks again!