Density and near-diagonal Dirac density matrix for closed shells of isotropic harmonically confined fermions in three dimensions

In early work, Lawes and March obtained a differential equation for an arbitrary number of independent harmonically confined fermions in one dimension, and very recently this result has been generalized to apply to three-dimensional (3D) isotropic harmonic confinement. Here, an exact solution of this 3D equation for the fermion particle density ρ(r) is constructed, and the near-diagonal form of the Dirac density matrix is also obtained. (author). Letter-to-the-editor