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.