  We consider a class of modified Schroedinger operators where the
semiclassical Laplacian is perturbed with h-dependent interface conditions
occurring at the boundaries of the potential's support. Under positivity
assumptions on the potential, we show that this modification produces a small
perturbation on the dynamics as h->0, independently from the time scale. In the
case of a time dependent potential, this yields uniform-in-h stability
estimates for products of instantaneous propagators. Then, following a standard
approach, the non-autonomous dynamical system is defined as a limit of stepwise
propagators and its small-h expansion is provided under suitable regularity
assumptions on the potential's variations.
