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However, it is shown here that, for every particle number N, there is an N-particle noninteracting kinetic-energy density functional T-N[rho], that is, a density functional that gives the noninteracting kinetic energy for N-particle densities, which is of first-degree homogeneity in the density rho((r) over bar). This gives a powerful tool, a strong requirement, for constructing such functionals. A systematic procedure to obtain the real part of T-N[rho], the full T-N[rho] in one-dimension, for each N is also proposed, It is pointed out, further, that in the Euler-Lagrange equations that determine the one-particle orbitals that define T-s[rho], the Lagrange multiplier that forces the orbitals to yield rho((r) over bar) is not other than the first derivative of T-s[rho], deltaT(s)[rho]/delta rho((r) over bar), which yields a natural derivation of the Kohn-Sham equations. Utilizing the same idea, it is shown for ground states how the Schrodinger equation can be derived from the basics of density-functional theory as well.", "digital" : null, "printed" : null, "sourceYear" : 2007, "foreignEdition" : true, "foreignLanguage" : true, "fullPublication" : true, "conferencePublication" : false, "nationalOrigin" : null, "missingAuthor" : false, "oaType" : "NONE", "oaCheckDate" : "2024-03-08", "oaFree" : false, "oaByAuthor" : { "otype" : "Author", "mtid" : 11, "link" : "/api/author/11", "label" : "Import Automata", "familyName" : "Import", "givenName" : "Automata", "published" : true, "oldId" : -1, "snippet" : true }, "citationCount" : 14, "citationCountUnpublished" : 0, "citationCountWoOther" : 14, "independentCitCountWoOther" : 8, "nationalOriginCitationCount" : 3, "foreignEditionCitationCount" : 14, "doiCitationCount" : 13, "wosCitationCount" : 12, "scopusCitationCount" : 9, "wosScopusCitationCount" : 12, "wosScopusCitationCountWoOther" : 12, 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