Some properties of the potential-to-ground state map in quantum mechanics

Abstract

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.

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Cited by in corpus (9)

• The structure of the density-potential mapping. Part I: Standard density-functional theory
• Universal Functionals in Density Functional Theory
• Building Kohn-Sham potentials for ground and excited states
• Seven Useful Questions in Density Functional Theory
• Density-potential inversion from Moreau-Yosida regularization
• Geometrical Perspective on Spin-Lattice Density-Functional Theory
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory