The Schrödinger-Poisson-Xα equation

Abstract

We deal with the inclusion of exchange effects in the self-consistent one particle Schrödinger equation. For the stationary case local approximations (of the Hartree-Fock equations) can be rigorously justified. By heuristically using these terms in the time dependent case we add the local exchange potential of the Xα method to the Hartree equations. Thus, we obtain the “Schrödinger-Poisson-Xα” model where the effective potential is the difference of the nonlocal Coulomb potential and the third root of the local density.