# 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.
1 Citations
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

## References

SHOWING 1-10 OF 67 REFERENCES
The geometry of classical and quantum fields
• 2019
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
The concentration-compactness principle in the calculus of variations. The locally compact case, part 2
• Mathematics
• 2019
-In this paper (sequel of Part 1) we investigate further applications of the concentration-compactness principle to the solution of various minimization problems in unbounded domains. In particular
Hohenberg–Kohn Theorems for Interactions, Spin and Temperature
We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any
Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian
We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p_{\rm loc}(\mathbb{R}^d)$, and with magnetic
Das Verhalten von Atomen im magnetischen Drehfeld
ZusammenfassungEs wird das Verhalten von frei drehbaren Atomen im zeitlich veränderlichen Magnetfeld untersucht. Insbesondere werden die infolge der Veränderung der Feldrichtung auftretenden