Figure 1
APS/Alan Stonebraker

Figure 1: Kohn-Sham potentials give the right electron density in an interacting system, even though the electrons are treated as independent particles. (Top) An example from the simplest system of interacting electrons: the helium atom. The top curve is the ground-state electron density. The lower curves show (orange) the nuclear potential, -2/r (in atomic units), that the electron lives in, and the (blue) Kohn-Sham potential, which is the potential in which noninteracting electrons yield the same density. (Bottom) Schematic of the time-dependent part of the Kohn-Sham potential (blue) of an electron wave packet (grey) propagating in a model semiconductor. The time-dependent part of the potential has a highly nonlocal dependence on the density: the potential to the left and right of the electron differ by a step, persisting far on either side. The size of the step oscillates in time. (For simplicity, modulations due to the lattice periodicity are omitted in the figure.)