Kinetic energy density and Pauli potential: dimensionality dependence, gradient expansions and non-locality

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Abstract
For arbitrary level filling, the fully non-local kinetic energy density and Pauli potential for the one-dimensional harmonic oscillator can be constructed explicitly. These exact results are eventually compared with the low-order gradient expansions. This prompts a fuller study of the dimensionality dependence of low-order gradient expansions for systems with general one-body potentials, and its relevance to the theory of the Pauli potential. One consequence of the present work is to display the generalization to D-dimensions as (D-2)/3D of the three-dimensional Kirzhnits coefficient (1957) 1/9 of the von Weizsacker term in the kinetic energy density.