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arXiv · 2609.13639

Sharp Dispersive Estimates for the Schrödinger Equation with an Attractive Coulomb Potential

Xitao Gao·Qiuye Jia·Junyong Zhang
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Abstract

We prove sharp dispersive $L^1 \to L^\infty$ estimates for the three-dimensional attractive Coulomb operator $H_Z=-Δ-Z|x|^{-1}$, where $Z>0$. The absolutely continuous part of the Schrödinger evolution decays at the free rate for short times, whereas its leading contribution decays like $|t|^{-1}$ for long times, with amplitude proportional to $Z$. This slower decay is driven by the threshold and is sharp when $Z^2|t|\gg1$.

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Xitao Gao, Qiuye Jia, Junyong Zhang. 2026-09-12. Sharp Dispersive Estimates for the Schrödinger Equation with an Attractive Coulomb Potential. https://arxiv.org/abs/2609.13639

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