Abstract
A general discussion of the single-particle density matrix in terms of the square root of the electron density ϱ( r) and phase factor for a given one-body potential V( r) of arbitrary symmetry for n occupied levels is given. The defining equations for the phase factor were obtained explicitly for the two-level case (e.g. LiH). By eliminating the one-body potential, a partial differential equation for the phase was obtained in terms of ϱ( r). Using the solution of this equation, the one-body potential can be expressed solely in terms of the ground-state density, to within an additive constant. The interest of these results with regard to density functional theory is emphasized.
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