Analytical description of some quantum systems with space- and time-periodic Hamiltonians

Electron movement in a spatially periodic high-frequency electric field is considered. If the spatial period is small enough and the frequency is sufficiently high, the effect of this field on the charged particle is in a sense equivalent to the effect of a time-independent effective potential that is a sequence of deep dynamic quantum wells where the electrons are confined. Also, a physical model is proposed which could be described in terms of such a Hamiltonian.