On a quantum heavy particle

We consider Schrödinger equation for a particle on a flat $n$-torus in a bounded potential, depending on time. Mass of the particle equals $1/\mu^2$, where $\mu$ is a small parameter. We show that the Sobolev $H^\nu$-norms, $\nu\geqslant1$ of the wave function grow approximately as $t^\nu$ on the time interval $t\in[0,t_*]$, where $t_*$ is slightly less than $O(1/\mu)$.