Suppose an electron in a crystal(periodic potential) has the Bloch wave function [itex]\psi (k_0,x)[/itex] at t=0. Applying a constant electric field E(at t=0), the electron would still have Bloch-type wave function at any time t with [itex]k(t)=-(1/\hbar) eEt+k_0[/itex]. Now According to this formula for k(t), one can see that k's are now continuous(wheras we had as many as N different ks in the first brillouin zone before exerting the electric field). Does electronic band structure change by applying the electric field or not? If yes, How?