In solid state physics you can calculate the band structure of a material, which is effectively the dispersion E_n(k), which depends on the wavevector as well as the band index. What I don't understand is this: Which states are occupied in a band? With this I mean: Which k values correspond to states actually occupied by electrons. Since k is continous it cannot be all k values since there is not an infinite number of electrons. For a plane wave dispersion I remember that you can use periodic boundary conditions to get a quantization of k in states that are actually occupied. How do you do this for a general dispersion, i.e. a general band structure?