Hartree-Fock

Consider the Hamiltonian of $N$ electrons interacting via a interaction potential $U$ which is constant and does not depend on the coordinates of the particles,

$$\hat{H} = \hat{\mathcal H}_0+\hat{U}\equiv \sum_{i=1}^N \hat{H}_0^{(i)}+ \frac{1}{2}\sum_{i\ne j}^N U.$$ (4.1)