  We prove some instability phenomena for semi-classical (linear or) nonlinear
Schrodinger equations. For some perturbations of the data, we show that for
very small times, we can neglect the Laplacian, and the mechanism is the same
as for the corresponding ordinary differential equation. Our approach allows
smaller perturbations of the data, where the instability occurs for times such
that the problem cannot be reduced to the study of an o.d.e.
