Commutator Estimates and Quantitative Local Weyl's Law for Schödinger Operators with Non-Smooth Potentials

• URL: http://arxiv.org/abs/2501.01381v1
• Date: Thu, 02 Jan 2025 17:52:06 GMT
• Title: Commutator Estimates and Quantitative Local Weyl's Law for Schödinger Operators with Non-Smooth Potentials
• Authors: Esteban Cárdenas, Laurent Lafleche,
• Abstract summary: We analyze Schr"odinger operators with potentials of class $C1,1/2$ and establish commutator estimates for the associated projection operators in Schatten norms. We study both non-interacting, and interacting particle systems.
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• Abstract: We analyze semi-classical Schr\"odinger operators with potentials of class $C^{1,1/2}$ and establish commutator estimates for the associated projection operators in Schatten norms. These are then applied to prove quantitative versions of the local and phase space Weyl laws in $L^p$ spaces. We study both non-interacting, and interacting particle systems. In particular, we are able to treat the case of the minimizers of the Hartree energy in the case of repulsive singular pair interactions such as the Coulomb potential.

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