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Tight Binding Model: mathematics

  1. Nov 15, 2014 #1
    From the textbook of Omar:

    nkIVr83.jpg

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

    Thanks in advance.
     
  2. jcsd
  3. Nov 15, 2014 #2

    mfb

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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".
     
  4. Nov 16, 2014 #3
    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
     
  5. Nov 16, 2014 #4

    mfb

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