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We consider eigenfunctions of a semiclassical Schr{\"o}dinger operator on aninterval, with a single-well type potential and Dirichlet boundary conditions.We give upper/lower bounds on the L^2 density of the eigenfunctions that areuniform in both semiclassical and high energy limits. These bounds are optimaland are used in an essential way in a companion paper in application to acontrollability problem. The proofs rely on Agmon estimates and a Gronwall typeargument in the classically forbidden region, and on the description ofsemiclassical measures for boundary value problems in the classically allowedregion. Limited regularity for the potential is assumed.

Uniform observation of semiclassical Schr{\"o}dinger eigenfunctions on an interval