Suppose that a static electric field is applied to an electron at time t=0, at which instant the electron is at the bottom of the band. Show that the position of the electron in real space at time t is given by , where x₀ is the initial position and F=-e is the electric force. Assume a one-dimensional crystal, and take the zero-energy level at the bottom of the band. Explain if the motion in real space is periodic.

x=x0 +RE(k = Ft / h) x=x0 +RE(k = Ft / h)