# Tight Binding Model: mathematics

From the textbook of Omar:

Can someone explain me the summation of this? I simply don't get it?

Related Atomic and Condensed Matter News on Phys.org
mfb
Mentor
Which summation do you mean?
The second equation is the first one with the argument that the sum over j' looks like "something"+"something"+...+"something" (N times the same summand) = N*"something".

Which summation do you mean?
The second equation is the first one with the argument that the sum over j' looks like "something"+"something"+...+"something" (N times the same summand) = N*"something".
I don't get how you go from the double summation to the new one with the new index etc.

Oh yeah i forgot to say: in the new expression they put Xj' = 0.

It's a function of the difference, Xj-Xj'. For each choice of j',the sum over j yields the same result. => I don't get it.

Also I don't get why you start from -N/2 and end with (N-1)/2

mfb
Mentor
Make an example. Write down all summands for N=5 and see how it works out.