Hohenberg–Kohn density-potential uniqueness conjecture

Let $H=T+V_{\mathrm{ee}}+V_{\mathrm{ext}}$ be the Hamiltonian of a bounded many-electron system, with external potential $v$ and one-particle density $n$ in a non-degenerate ground state. The Hohenberg–Kohn conjecture. The density $n$ uniquely determines the external potential $v$ modulo an additive constant. This is the density-potential mapping underlying ground-state density functional theory. The source presents the statement as a conjectural, non-rigorous formulation of the Hohenberg–Kohn theorem and does not provide a resolution of its stated hypotheses.