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arXiv · 2606.26581

Determining potentials from the scattering map of the time-dependent Schr\"odinger equation

Qiuye Jia
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Abstract

For a time dependent Schr\"odinger equation, the scattering map is the map sending the asymptotic profile of a solution as $t \to-\infty$ to its asymptotic profile as $t\to+\infty$. In this paper we show that, for a certain class of metrics, the scattering maps and Poisson operators associated to two Schr\"odinger operators on the same curved space only differ by a compact operator on a critical level if and only if the two potentials are equal.

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Qiuye Jia. 2026-06-25. Determining potentials from the scattering map of the time-dependent Schr\"odinger equation. https://arxiv.org/abs/2606.26581

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