Some Properties of the Potential-to-Ground State Map in Quantum Mechanics

@article{Garrigue2021SomePO,
  title={Some Properties of the Potential-to-Ground State Map in Quantum Mechanics},
  author={Louis Garrigue},
  journal={Communications in Mathematical Physics},
  year={2021}
}
  • Louis Garrigue
  • Published 7 December 2020
  • Mathematics
  • Communications in Mathematical Physics
We analyze the map from potentials to the ground state in static many-body quantum mechanics. We first prove that the space of binding potentials is path-connected. Then we show that the map is locally weak-strong continuous and that its differential is compact. In particular, this implies the ill-posedness of the Kohn-Sham inverse problem. 
Building Kohn–Sham Potentials for Ground and Excited States
  • Louis Garrigue
  • Mathematics
    Archive for Rational Mechanics and Analysis
  • 2022
. We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given k and a target density ρ , there exist potentials having k th excited

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Building Kohn–Sham Potentials for Ground and Excited States
  • Louis Garrigue
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    Archive for Rational Mechanics and Analysis
  • 2022
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