One of the most common ways of dealing with the many-fermion problem
is to assume that each electron can be considered separately. Each
electron is treated as moving in a mean field potential, 
. This
potential models the effects of all the other particles in the system,
as well as any external potential acting on the system.
The one-electron equations are of the form
where 
is a one-electron wavefunction and 
are Lagrange multipliers which arise from the fact that the
one-electron wavefunctions are normalised. Choosing an appropriate
for the single electron is still a very complicated
problem. depends upon the interactions between the electrons
and therefore on the one-electron wavefunctions. Since initially
neither of these quantities, or , is known, it is
necessary to solve Eq.(
) in a self-consistent manner.
