UPSILON-REPRESENTABILITY FOR SYSTEMS OF A FEW FERMIONS

The upsilon-representability of the particle density for a system of noninteracting fermions is considered. It is shown that any reasonable spherical density for two spinless fermions is either the nondegenerate ground-state density or a linear combination of degenerate ground-state densities for some effective local potential, and is therefore ensemble upsilon-representable. The results of model calculations are given that illustrate various possible situations for two-particle systems. An extension of this result for systems of more particles is made and the implications for density-functional theory are discussed.