Kinetic energy density study of confined noninteracting fermions: The importance of the angular momentum

In this work we present a study of the kinetic energy density of an arbitrary number of noninteracting fermions confined in a Coulombic potential. We present the results for the total kinetic energy and the kinetic energy density using three simple but representative functionals: Thomas-Fermi, von Weizsaker, and the second order gradient expansion approximation. In order to assess their quality, the deviation of the kinetic energy density of every functional is measured through a parameter that reflects the quality of the functionals in a better way than their relative errors (for that reason, we call it quality factor). Trying to understand the performance of the different functionals we study degenerate states with the same energy but different angular momenta and densities. Therefore, the functionals' ability to capture the effects of each density corresponding to the different angular momenta is discussed, as well as the trends of these contributions.