A solid with electrons localized on lattice sites is often modeled by so- called "tight-binding" model. In this 1D model the dispersion relation is E(k) = −2E cos(ka), where a is the lattice constant. Starting from the effective equation of motion, describe how the electron moves in such a model under the influence of the constant electric field. Assume you measure electrical current as a function of time without any scat- tering. You will find an oscillatory behavior for the current. What is the frequency of this current? This is not observed in practice because scattering will exist.

A solid with electrons localized on lattice sites is often modeled by so- called "tight-binding" model. In this 1D model the dispersion relation is E(k) = −2E cos(ka), where a is the lattice constant. Starting from the effective equation of motion, describe how the electron moves in such a model under the influence of the constant electric field. Assume you measure electrical current as a function of time without any scat- tering. You will find an oscillatory behavior for the current. What is the frequency of this current? This is not observed in practice because scattering will exist.