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Fourier transform operators

  1. Dec 29, 2013 #1
    1. The problem statement, all variables and given/known data
    The exercise is a) in the attached trial. I have attached my attempt at a solution, but there are some issues. First of all: Isn't the example result wrong? As I demonstrate you get a delta function which yields the sum I have written (as far as I can see), not the sum written in the trial. Secondly, what am I supposed to do in the sum for H_el, where I have a double-sum of position coordinates. I would like to somehow get a delta function, but the exponential is zero whenever k1*Ri=k2*Rj, which I can't translate into a delta function.
    Also I am very confused why the fourier series in position variables is given for x and p when clearly they enter in the original hamiltonian as creation and anihillation operators for position coordinates.

    2. Relevant equations



    3. The attempt at a solution
    Attached
     

    Attached Files:

    Last edited: Dec 29, 2013
  2. jcsd
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