区间上半经典薛定谔本征函数的一致观测

IF 0.8 Q2 MATHEMATICS Tunisian Journal of Mathematics Pub Date : 2022-03-07 DOI:10.2140/tunis.2023.5.125
Camille Laurent, Matthieu Léautaud
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引用次数: 6

摘要

我们考虑半经典Schr的本征函数区间上的dinger算子,具有单阱型势和Dirichlet边界条件。我们给出了本征函数的L^2密度的上/下界,这些本征函数在半经典和高能极限下都是一致的。这些边界是最优的,并且在应用于可控性问题的配套论文中以重要的方式使用。证明依赖于经典禁域中的Agmon估计和Gronwall型论证,以及经典允许域中边值问题的半经典测度的描述。假设电势具有有限的规律性。
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Uniform observation of semiclassical Schrödinger eigenfunctions on an interval
We consider eigenfunctions of a semiclassical Schr{\"o}dinger operator on an interval, with a single-well type potential and Dirichlet boundary conditions. We give upper/lower bounds on the L^2 density of the eigenfunctions that are uniform in both semiclassical and high energy limits. These bounds are optimal and are used in an essential way in a companion paper in application to a controllability problem. The proofs rely on Agmon estimates and a Gronwall type argument in the classically forbidden region, and on the description of semiclassical measures for boundary value problems in the classically allowed region. Limited regularity for the potential is assumed.
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
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