I have a small question about the calculation of the off diagonal elements
<\psi_1| H | \psi_2>. Making the calculation gives me:
-\lambda \int e^{ikx} \sum \delta(x+na) e^{-i[k-2\pi/a]x}dx.
working out this equation gives me:
-\lambda \int e^{2\pi xi/a} \sum \delta(x+na)dx
from now on I am a bit stuck on how to evaluate this integral and find the solution of -\lambda /a
Firstly, do specify the integral limits and the indices over which summation goes. Then, to evaluate the integral itself, check the properties of the delta-function.