发表机构
Beijing Institute of Technology; City University of Hong Kong（北京理工大学; 香港城市大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究一维薛定谔方程在势能 $|x|$ 下的可观测集，证明可测集在任意正时刻可观测当且仅当它是厚的，并给出观测常数的一致性，回答了厚集与可观测集关系的问题。
AI 中文摘要
本文研究一维薛定谔方程在算子 $H=-d^2/dx^2+|x|$ 于 $L^2(\mathbb R)$ 上的可观测集。我们证明：一个可测集在任意正时刻可观测当且仅当它是厚的。对于每个固定的观测时间，可观测常数在所有具有给定厚度参数的集合上是一致的。该定理回答了 Gengsheng Wang [12] 针对此非谐振子提出的关于厚集与可观测集之间关系的问题。
英文摘要
In this paper, we study observable sets for the one-dimensional Schrödinger equation associated with the operator $H=-d^2/dx^2+|x|$ on $L^2(\mathbb R)$. We prove that a measurable set is observable at every positive time if and only if it is thick. For each fixed observation time, the observability constant is uniform over all measurable sets with prescribed thickness parameters. The theorem answers the question concerning the relationship between thick and observable set raised by Gengsheng Wang [12] for this anharmonic oscillator.
