  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.
