Abstract
Density functionaltheoryforthecaseofgeneral, N-representabledensitiesisreformulatedintermsof
density functionalderivativesofexpectationvaluesofoperatorsevaluatedwithwavefunctionsleading
to adensity,makingnoreferencetotheconceptofpotential.Thedevelopmentsprovideproofofex-
istence ofamathematicalprocedurethatdetermineswhetheradensityis v-representableandinthe
case ofanaffirmativeanswerdeterminesthepotential(withinanadditiveconstant)asaderivativewith
respect tothedensityofaconstrainedsearchfunctional.Italsoestablishestheexistenceofanenergy
functional ofthedensitythat,for v-representabledensities,assumesitsminimumvalueatthedensity
describing thegroundstateofaninteractingmany-particlesystem.ThetheoremsofHohenbergand
Kohnemergeasspecialcasesoftheformalism.Numericalresultsforone-dimensionalnon-interacting
systemsillustratetheformalism.Somedirectformalandpracticalimplicationsofthepresentre-
formulation ofDFTarealsodiscussed.
