One starts with the independent particle (IP) approximation. Let
the wave function
where
can be expressed as a Slater determinant,
Now apply the variational procedure to such a function as a trial
function. In addition, we require that the single particle functions
be orthonormalized, i.e.,
Then we can write the variational principle as,
This gives a set of non-linear integro-differential equations known as the Dirac-Fock SCF equations. (See the next chapter for more details on the variational procedure)