ON THE SINGLE-PARTICLE KINETIC-ENERGY DENSITY FUNCTIONAL IN HYPERSPHERICAL REPRESENTATION

The properties of hyperspherical representation where the one-body orbitals are expressed in terms of the square root of the electron density, rho(r) and the angle functions {theta-i(r)}i = 1,...,N-1, (R.F. Nalewajski, P.M. Kozlowski, Acta Phys. Pol. A74, 287 (1988)) are discussed, and the expression for the kinetic energy density functional is analyzed. This expression contains the Weizsacker term plus a correction determined by the angle functions. Taking into account both the limit of only one occupied level and the slowly varying electron density with large N, it is shown that the kinetic energy density functional interpolates correctly between the known results. Finally, an example of a linear harmonic oscillator is given and the relation between the usual orbital pictures is discussed.