How does DFT handle degenerate eigenvectors?

[Mart1234]

TL;DR Summary

DFT and degeneracy

I have a question about how DFT (density functional theory) handles degenerate states. The Hamiltonian in DFT is a functional of the electron density defined via $n(\mathbf{r})=\sum^N_{k=1}|\psi_k(\mathbf{r})|^2$. However, say I have a pair of degenerate states. Then any linear combination of these two states is also a solution to the Kohn-Sham equations and the electron density based on the above definition seems to be not well defined. How does DFT address this? Is there a constraint for degenerate states which picks a proper orientation?

 

[DrDu]

Hm, each of the degenerate states has it's own density. E.g. if degeneracy is due to rotational degeneracy, as an example, psi might be a p orbital. As they are degenerate, the orbital can point in any direction and the corresponding electronic density will be concentrated along the same direction.