1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Many body 2nd order energy shift of ground state
  1. 1D Ising ground state (Replies: 0)

Loading...