In search of the Hohenberg-Kohn theorem

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The Hohenberg-Kohn theorem, a cornerstone of electronic density functional theory, concerns uniqueness of external potentials yielding given ground densities of an N-body system. The problem is rigorously explored in a universe of three-dimensional Kato-class potentials, with emphasis on trade-offs between conditions on the density and conditions on the potential sufficient to ensure uniqueness. Sufficient conditions range from none on potentials coupled with everywhere strict positivity of the density to none on the density coupled with something a little weaker than local 3N/2-power integrability of the potential on a connected full-measure set. A second theme is localizability, that is, the possibility of uniqueness over subsets of R3 under less stringent conditions.

Original languageEnglish (US)
Article number042110
JournalJournal of Mathematical Physics
Issue number4
StatePublished - Apr 1 2018

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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