Building Kohn–Sham Potentials for Ground and Excited States

  title={Building Kohn–Sham Potentials for Ground and Excited States},
  author={Louis Garrigue},
  journal={Archive for Rational Mechanics and Analysis},
  • Louis Garrigue
  • Published 4 January 2021
  • Mathematics
  • Archive for Rational Mechanics and Analysis
. 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 mixed states which densities are arbitrarily close to ρ . The state can be chosen pure in dimension d = 1 and without interactions, and we provide numerical and theoretical evidence consistently leading us to conjecture that the same pure representability result holds for d = 2 , but that the set of… 
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