Density amplitude equation of inhomogeneous electron liquid: A route via Hartree-Fock density matrix

The effective potential entering the Schrodinger equation For the ground-state density amplitude of an inhomogeneous electron liquid is shown to be a unique functional of the Hartree-Fock density matrix, the functional being known. However, this would only become a density Functional theory if the Hartree-Fock density matrix could be written as a functional of the exact ground-state density. This is also shown to be true, at least in principle.