Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Chen, Lu, Liu, Haolin, Liu, Hongyu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6591708273
OpenAlex ID: W7220990725