Unique continuation for many-body Schrodinger operators and the Hohenberg-Kohn theorem

Louis Garrigue (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We prove the strong unique continuation property for many-body Schrodinger operators with an external potential and an interaction potential both in $L^p_{loc}(\mathbb{R}^d)$, where p > max(2d/3, 2), independently of the number of particles. With the same assumptions, we obtain the Hohenberg-Kohn theorem, which is one of the most fundamental results in Density Functional Theory.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Chimie théorique et/ou physique

Louis Garrigue. Unique continuation for many-body Schrodinger operators and the Hohenberg-Kohn theorem. Mathematical Physics, Analysis and Geometry, 2018, 21 (3). ⟨hal-01770288v4⟩