Abstract
We prove the strong unique continuation property for many-body Schrödinger operators with an external potential and an interaction potential both in \(L^{p}_{\text {loc}}(\mathbb {R}^{d})\), where p > 2 if d = 3 and \({p = \max (2d/3,2)}\) 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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Acknowledgements
I warmly thank Mathieu Lewin, my PhD advisor, for having supervised me during this work. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement MDFT No 725528).
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Garrigue, L. Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. Math Phys Anal Geom 21, 27 (2018). https://doi.org/10.1007/s11040-018-9287-z
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DOI: https://doi.org/10.1007/s11040-018-9287-z