  The purpose of this note is to investigate the high frequency behaviour of
solutions to linear Schr\"odinger equations. More precisely, Bourgain and
Anantharaman-Macia proved that any weak-* limit of the square density of
solutions to the time dependent homogeneous Schr\"odinger equation is
absolutely continuous with respect to the Lebesgue measure on $R\times T^d$.
Our contribution is that the same result automatically holds for non
homogeneous Schr\"odinger equations, which allows for abstract potential type
perturbations of the Laplace operator.
