The role of the von Weizsacker kinetic energy gradient term in independent harmonically confined fermions for arbitrary two-dimensional closed-shell occupancy

The search for the single-particle kinetic energy functional TS[n] continues to be of major interest for density functional theory. Since it is expected to be generally applicable, exactly solvable models are of obvious interest. Here we focus on one, which is also of interest experimentally in magnetic trapping of ultracold fermion vapours. This is the model of independent harmonically trapped fermions in two dimensions. Here, the role of the von Weizsäcker inhomogeneity kinetic energy is a focal point, prompted also by the work of Delle Site (2005 J. Phys. A: Math. Gen. 38 7893).