A one-to-one mapping between one-particle densities and some n-particle ensembles

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Abstract
A one‐to‐one mapping between the one‐particle densities and a particular set of n‐particle ensembles is constructed. The construction entails simultaneous minimization of the energy and minimization of the L2‐norm over the set of ensembles which yield a given density. Differences between the present approach to density functional theory and other approaches, such as Kohn–Sham theory (Ref. 12) and Thomas–Fermi–Dirac–Weizsacker theory (Ref.13) are emphasized. The Levy density functional may be decomposed into kinetic and electron–electron interaction components.