Dependence of current on energy for the integral quantum Hall effect

The dependence of the Hall-current on energy of a 2-D electron system in a strong perpendicular magnetic field is studied using sum rule arguments. It turns out that, in a finite system, this dependence is determined to a large extent by the states at the edges of the system. As a consequence the distance between the mobility edges is considerably smaller than the width of the density of states. In fact the mobility edges are essentially the same as in the unperturbed system.