# Evaluating the Coulomb Integral for a two-electron atom

1. Apr 1, 2014

### yelneerg

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

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 $\frac{1}{\left|\vec{r}_1-\vec{r}_2\right|}$ bit?

2. Apr 1, 2014

### yelneerg

I think I may need to use variational principle?