# Homework Help: Eigenvalue of Exchange Operator in Hartree-Fock: 2e-

1. Nov 4, 2017

### avkr

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

2. Relevant equations

3. The attempt at a solution

$\hat{S}_1.\hat{S}_2 = (S(S+1) - S_1(S_1 + 1) - S_2(S_2 + 1))/2$
therefore singlet: $\psi_s = \frac{\phi_a (1)\phi_b(2)(\alpha(1)\beta(2) - \alpha(2)\beta(1))}{\sqrt(2)}$
So for singlet,
$\mathcal{V} = -\frac{K \psi_s}{2} - 0$

I need help in calculating in $\frac{K \psi_s}{2}$

2. Nov 9, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.