Corrections to Thomas-Fermi densities at turning points and beyond

Phys Rev Lett. 2015 Feb 6;114(5):050401. doi: 10.1103/PhysRevLett.114.050401. Epub 2015 Feb 4.

Abstract

Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many noninteracting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the leading corrections to Thomas-Fermi theory, involve neither sums nor derivatives, are spatially uniform approximations, and are exceedingly accurate.