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Homework Help: Many body 2nd order energy shift of ground state

  1. Nov 12, 2012 #1
    This is more of a math question I suppose, but its in the context of calculating the second order energy shift in the ground state energy for a non relativistic collection of electrons.

    We end up showing that the energy shift has a finite and divergent piece. The divergent bit is proportional to the following:

    [tex]
    f(q) = \int_{|k+q|>1} d^3k \int_{|p+q|>1} d^3p \frac{\theta(1-k) \theta(1-p)}{q^2 + \vec{q} \cdot ( \vec{k} + \vec{p} ) }
    [/tex]

    The part I'm getting stuck on is showing that

    [tex] f(q) \approx \frac{2}{3}(2\pi)^2(1-ln2)q [/tex]

    as q approaches zero. I've tried a bunch of things, but to no avail. Any suggestions?
     
    Last edited: Nov 12, 2012
  2. jcsd
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