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Statements utilized or mentioned in the Part I are proved or discussed in detail. Especially it is shown that for finite-dimensional state spaces the strictly positive densities being strictly less than two are E-V representable and that the density functional by Lieb is differentiable at the E-V densities.Aussagen, die im Teil I benutzt oder erwahnt wurden, werderi bewiesen bzw. im Detail diskutiert. Insbesondere wird gezeigt, daB fur endlichdimensionale Zustttndsraume die strikt positiven Dichten, die strikt kleiner als zwei sind, E-V-erzeugbar sind sowie daB das Dichtefunktional von Lieb genau an den E-V-Dichten differenzierbar ist.The exact density functionals and several types of representability of one-particle densities have been introduced in Part I (Section 2) of this paper; for references [l to 221 also confer Part I. 'V-RepresentabilityThe distinction between E-, PS-, andD-V densities makes sense, since not every density For finite-dimensional state spaces, however, it has been proved for bosons in [23] that every strictly positive density is PS-V representable and the corresponding conjecture for fermions has been posed in the same paper. This conjecture can indeed be shown [24] by refining the considerations in [23], but we want to deal here with an essentially shorter proof.Theorem 5.1. For finite-dimensional state spaces every strictly positive density n ( r ) < 1 (or < 2 for spin degeneracy 2) is a fermion E-V density.Proof. We consider a system of N fermions (for notational convenience without spin degeneracy), where every particle has the state space RQ; q > N . The functional F,(n) as defined by (2.10) is convex. Hence, F,(n) has a continuous tangent functional at every ?z in the interior of the set of all fermion densities 8, = {(n(l), ... , %(a)) : 0 5 5 n ( r ) 5 1, C n ( r ) = N } . In the proof of theorem 6.1 we show that F L ( n ) possesses a continuous tangent functional exactly at E -V densities. Therefore, all densities from the interior of S, are E -V representable.

The exact one-particle density functionals by Levy and Lieb for the calculation of pound-state energies are analysed. A method for the calculation of the Levy-Lieb functional is proposed.Based on a work by Lieb, the range of validity of the exact self-consistent equations by Kohn and Sham is determined. A self-consistent procedure which is applicable in a wider range is presented.Die exakten Einteilchendichtefunktionale von Levy und Lieb zur Berechnung von Grundzustandsenergien werden analysiert. Eine Methode zur Berechnung des Levy-Lieb-Funktionals wird vorgeschlagen. Lieb folgend wird der Giiltigkeitsbereich der exakten selbstkonsistenteii Gleichungen von Kohn und Sham bestimmt. Es wird ein selbstkonsistentes Verfahren vorgestellt, das in einem groDeren Bereich anwendbar ist.

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