In the Hartree equation above, represents the energy contribution of electron . The term represents the potential due to the other electrons in which electron moves. In this equation we can formally see the effect of screening by the other electrons. The equation is derived (see Gasiorowicz pp 309-311) from the Schrödinger equation using . Since we will not apply these equations to solve problems, we will not go into the derivation, however, it is useful to know how one might proceed to solve more difficult problems.

An improved formalism known as the Hartree-Fock equations, accounts for the required antisymmetry and gives slightly different results.

Jim Branson 2013-04-22