Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem

@article{Garrigue2018UniqueCF,
  title={Unique Continuation for Many-Body Schr{\"o}dinger Operators and the Hohenberg-Kohn Theorem},
  author={Louis Garrigue},
  journal={Mathematical Physics, Analysis and Geometry},
  year={2018},
  volume={21},
  pages={1-11}
}
  • Louis Garrigue
  • Published 20 April 2018
  • Mathematics
  • Mathematical Physics, Analysis and Geometry
We prove the strong unique continuation property for many-body Schrödinger operators with an external potential and an interaction potential both in Llocp(ℝd)$L^{p}_{\text {loc}}(\mathbb {R}^{d})$, where p > 2 if d = 3 and p=max(2d/3,2)${p = \max (2d/3,2)}$ otherwise, 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. 
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