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For a two-level problem in one dimension, an implicit relation is derived relating the kinetic energy density t_{s}(x) to the electron density ρ(x) plus its first and second derivatives. As an example, the harmonic oscillator potential is used to make this relation explicit.
The properties of hyperspherical representation where the one-body orbitals are expressed in terms of the square root of the electron density, ρ(r) and the angle functions {θ_{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 Weizsäcker term plus...
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