Suppose that a static electric field E is applied on a conductive crystal. Then, how quantum mechanics describes the electron movements in the crystal? I have been trying to find an explanation, but have not found any. As I understand it, we could treat the E field as a time-dependent perturbation, starting at t=0. But after sufficient time E would not excite any electron to any higher energy level. However, if the electron's wavefunction is a combination of more than one Bloch functions/states, then the perturbation of E can excite the electrons to different ones of these Bloch states, which could be an origin of electron conduction in crystal. One question, however, is that such excitation is "symmetrical", that is, it is not directional as the E field is. Is there any problem with these considerations?