I am reading a lot about how to calculate band bending from solving the Schrödinger equation and Poisson equation self-consistently. To recap some of the central ideas are: We look at the conduction band of some semiconductor. If we assume that the electrons are free electrons with some effective mass m*, we can solve the Schrödinger equation and calculate the electrondensity. This can then be used to determine the electrostatic potential, which can be plugged back in to the Schrödinger equation and this process can then be carried on until a self-consistent solution is found. Now some things bother me about this approach. It is assumed that electrons in the conduction band only interact with other electrons in the conduction band and not electrons in any of the filled bands. Why are the electrons in these bands inert? Does this follow from solving the full many-body problem? I don't exactly remmeber how band structure comes about, but I think one uses the periodicity of the coulomb potential from the static ions to show that this creates bands.