Non-local kinetic energy functional for an arbitrary number of Fermions moving independently in one-dimensional harmonic oscillator potential

For one-dimensional Fermions bound by a general one-body potential V(x), th e Pauli potential is first related to the kinetic energy and the particle d ensity rho(x). For the model of the harmonic oscillator, V(x) = 1/2x(2), th is equation leads to a non-local kinetic energy functional in which only fi rst-order derivatives of rho(x) enter. This example shows the usefulness of a new concept, the Pauli function, which encompasses the Pauli principle i n terms of the electronic density. For the harmonic oscillator model, the k inetic energy can then be expressed exactly in terms of the Thomas-Fermi ki netic energy functional, together with the von Weizsacker inhomogeneity ter m, but now in a fully non-local way. (C) 2000 Published by Elsevier Science B.V. All rights reserved.