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arXiv · 2607.12852

A maximal Hohenberg-Kohn theorem for non-interacting systems via potential theory

Thiago Carvalho Corso
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Abstract

We show that for Schr\"odinger operators in a connected domain, the Hohenberg-Kohn theorem holds within the class of Laplace form-bounded external potentials if and only if the single-particle density is strictly positive quasi-everywhere. Furthermore, we show that this condition is satisfied for non-interacting Schr\"odinger operators whenever a ground-state exists. Consequently, we establish the Hohenberg-Kohn theorem for non-interacting systems, and thereby the uniqueness of the Kohn-Sham potential, within the maximal class of Laplace form-bounded distributions. The main ingredient to establish these results is a characterization of regular states, whose proof relies on tools from classical potential theory. Moreover, this characterization reveals that, in the continuum setting, the fundamental mechanism underlying the Hohenberg-Kohn theorem is the (quasi)-unique continuation of the density rather than of the many-body wavefunction.

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Thiago Carvalho Corso. 2026-07-14. A maximal Hohenberg-Kohn theorem for non-interacting systems via potential theory. https://arxiv.org/abs/2607.12852

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