# Tight Binding Model: mathematics

From the textbook of Omar:

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

## Answers and Replies

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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.