Hartree equations

In solid-state physics and quantum chemistry, the Hartree equations or the self-consistent field approximation are a set of non-linear equations used to study many-electron systems inside a metal. These quantum mechanical equations are self-consistent, meaning that the solutions can be found by iteration. These approximation is the result of a mean-field theory that describes one electron interacting with a field that is the result of averaging the position of the rest of electrons. The equations are named after Douglas Hartree, who introduced them in 1927.

Hartree method is one of the main ingredients of Hartree–Fock method, which improves on Hartree equations by including the exchange interaction.