I know that it is impossible for real electrons and nuclei. In the Kohn and Sham approach, a system of interacting electrons is approximated by a system of non-interacting Kohn-Sham particles in an effective potential.
My question refers not to a real chemical system. Rather, I am asking about a system of toy particles that don't necessarily correspond to reality.
Is there such a system of multiple interacting quantum particles for which density can be obtained analytically for arbitrary number of particles, at least in terms of some special functions, say, hypergeometric functions?
The particles may be point particles, they may interact not necessarily at contact, may be only pairwise interactions, maybe in 1D, etc.