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

@misc{gao2026sharp,
  title = {{Sharp Dispersive Estimates for the Schrödinger Equation with an Attractive Coulomb Potential}},
  author = {Xitao Gao and Qiuye Jia and Junyong Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13639},
  eprint = {2609.13639},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13639},
}

TY  - UNPB
TI  - Sharp Dispersive Estimates for the Schrödinger Equation with an Attractive Coulomb Potential
AU  - Xitao Gao
AU  - Qiuye Jia
AU  - Junyong Zhang
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13639
UR  - https://arxiv.org/abs/2609.13639
AB  - We prove sharp dispersive L^1 → L^∞ 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|≫1.
ER  -