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Evaluating the Coulomb Integral for a two-electron atom

  1. Apr 1, 2014 #1
    1. The problem statement, all variables and given/known data

    Evaluate the so-called Direct (or Coulomb) Integral, C, which occurs in the theory of the 2-electron atom.

    C=[itex]\int\int d\vec{r}_1d\vec{r}_2\left|\phi_a(1)\right|^2\left|\phi_b(2)\right|^2 \frac{e^2}{\left|\vec{r}_1-\vec{r}_2\right|}[/itex]

    You may assume that both particles are in the ground state.

    2. Relevant equations


    3. The attempt at a solution

    I'm really just at a loss as to how to get started. I'm guessing that being in the ground state simplifies something. Maybe expand the [itex]\frac{1}{\left|\vec{r}_1-\vec{r}_2\right|}[/itex] bit?
  2. jcsd
  3. Apr 1, 2014 #2
    I think I may need to use variational principle?
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