Electron degeneracy pressure Why is it that in stars undergoing gravitational collapse electron degeneracy kicks in? Why couldn't the electrons form energy bands like in semiconductors? 
 A: Quantised energy levels/bands arise from electrons moving in a potential well. In say a white dwarf, the degenerate electrons can have kinetic energies of order 100-keV to 1MeV and can usually be assumed to behave like (almost) free particles. In which case there are a set number of available momentum eigenstates per unit volume
$$ g(p)\,dp = \frac{8 \pi p^2}{h^3}\,dp ,$$
where $p$ is the momentum. The electrons fill up all the available energy states (because of the Pauli exclusion principle) up to the Fermi momentum/energy.
There are small corrections made to account for the fact that positive charge is concentrated in nuclei whilst the electrons are (almost) uniformly distributed (electrostatic corrections). Below densities of $10^{7}$ kg/m$^3$ (brown dwarfs, planets) the assumption of a uniform electron distribution breaks down, the Fermi (kinetic) energies move to an atomic scale and further corrections need to be made (Thomas-Fermi corrections) which assume the electrons move in the spherically symmetric potential of a nucleus. 
