  Our aim in this work is to give some quantitative insight on the dispersive
effects exhibited by solutions of a semiclassical Schr{\"o}dinger-type equation
in R d. We describe quantitatively the localisation of the energy in a
long-time semiclassical limit within this non compact geometry and exhibit
conditions under which the energy remains localized on compact sets. We also
explain how our results can be applied in a straightforward way to describe
obstructions to the validity of smoothing type estimates.
