  We consider quantum dynamics of systems with fast spatial modulation of the
Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and
decoupling fast and slow spatial oscillations we demonstrate that the effective
dynamics is governed by a Schr\"{o}dinger-like equation of motion and obtain
the expression of the resulting effective Hamiltonian. In particular, we show
that there exists an attractive effective potential even in the case when the
oscillating potential averages to zero.
