I'm teaching myself how to do DFT for my master's project, where I want to use it for calculating band structures for different heterostructures. Now to learn DFT I am on one hand reading a book on the basic theory, on the other hand using different freeware packages to try and calculate the band structure for some simple systems like bulk silicon. One thing that bothers me however, is how to connect the theory I learn in the book, with how the program works. As far as I can understand the idea of DFT is to map a many body problem to a non-interacting problem, using some exchange correlation function, which will produce the same ground state density. To do so a range of methods like the LDA and different choices for the xc-potential is avaiable. However, I don't understand how to basically go from a theory that allows you to calculate the ground state density to the band structure. Band structure is basically the dispersion of the energy of your system, i.e. E(k), which, for a noninteracting electron gas for example, is a parabola. But how can I get this from the ground state density? I think the Kohn-sham eigenvalues are not the true eigenvalues of the system and neither are the kohn-sham orbitals.