v-representability for systems of a few fermions

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Abstract
The v-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 v-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.