Hartree Fock theory for Electron gas in the mean field regime

Abstract

The goal of this thesis is to explore the Hartree Fock ground state energy in the mean field approximation under Coulomb interaction. It was earlier believed that free Fermi gas energy is the true ground state energy in Hartree Fock approximation but Overhauser showed that there exists a state with energy lower than free Fermi gas energy. The question we explore in this thesis is whether we can multiply Coulomb potential by a small constant such that for any interaction with coupling parameter less than this constant, free Fermi gas energy is the true ground state energy and any interaction with coupling parameter greater than this constant, there exists some other state with energy lower than free fermi gas energy. We were able to derive a partial result in this direction proving that there exists some small constant such that free fermi gas energy is the true ground state energy in Hartree Fock approximation.