Time evolution of a Bloch electron in a constant electric field

We describe the time evolution of a Bloch electron in a constant electric field in terms of electric-field-dependent Bloch functions. These basis functions take into account the equivalent (periodic) electric-field-induced alteration of each of the electronic potential wells of the crystal. In this scheme, all interband matrix elements vanish. As a result, we obtain a relatively simple expression for the time evolution of an electron in a periodic potential under the influence of a constant electric field.