  We study the Schr\"odinger equation on $\R$ with a potential behaving as
$x^{2l}$ at infinity, $l\in[1,+\infty)$ and with a small time quasiperiodic
perturbation. We prove that, if the perturbation belongs to a class of
unbounded symbols including smooth potentials and magnetic type terms with
controlled growth at infinity, then the system is reducible.
