Quote by sam_bell
If by "natural" you mean the *eigenstates* of the interacting electron system, then no. But you could take Slater determinants of the sine wave solutions as a useful *basis* to work in for the interacting electron problem. If you really want to find a good ground state though, probably the best approach would be to use a test wavefunction with a few free parameters and apply the variational principle.

Natural orbitals are defined technically as the orbitals which diagonalize the 1density operator.