Uniform observation of semiclassical Schrödinger eigenfunctions on an interval - Sorbonne Université
Journal Articles Tunisian Journal of Mathematics Year : 2023

Uniform observation of semiclassical Schrödinger eigenfunctions on an interval

Abstract

We consider eigenfunctions of a semiclassical Schrödinger 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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Dates and versions

hal-03597902 , version 1 (04-03-2022)
hal-03597902 , version 2 (19-09-2022)

Identifiers

Cite

Camille Laurent, Matthieu Léautaud. Uniform observation of semiclassical Schrödinger eigenfunctions on an interval. Tunisian Journal of Mathematics, 2023, 5 (1), pp.125-170. ⟨10.2140/tunis.2023.5.125⟩. ⟨hal-03597902v2⟩
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