In my experience with (Kohn-Sham) density functional theory, the external potential is due to a massive particle like a nucleus or ion. I have never seen an electron be the source of the potential, and I wonder why. For instance, if I want to study the electron gas model using DFT, it seems entirely natural to imagine the gas's response to an additional electron placed at the origin. However, I can imagine two objections to this procedure:
- The Heisenberg uncertainty principle prevents us from knowing that the inserted electron is both at the origin and at rest.
- Because electrons are identical fermions, we are not allowed to single one of them out as being the source of the external potential.
Neither of these are practical issues in the case where the external potential is due to a heavy particle. Do either of these objections (or possibly others that I haven't thought of) mean that an external potential in DFT cannot be sourced by an electron?