Tight Binding Model: mathematics

  • Thread starter Waxterzz
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  • #1
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From the textbook of Omar:

nkIVr83.jpg


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

Thanks in advance.
 

Answers and Replies

  • #2
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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".
 
  • #3
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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
 
  • #4
34,962
11,147
Make an example. Write down all summands for N=5 and see how it works out.
 

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