Approximate Bounds to the Average Electron Momentum Densityfor Atomic Systems

Abstract

Approximate bounds to the average electron momentum density⟨γ⟩ in terms of momentum expectation values⟨pn⟩ have been derived for atomicsystems. These bounds are based on the semiclassical relationships inthe Thomas–Fermi model. Meanwhile, approximate bounds to theaverage electron density ⟨ρ⟩ in terms of the expectationvalues ⟨rn⟩ have also been obtainedemploying a similar procedure on the basis of the same model. Thequality of the bounds presented is numerically studied and discussedwithin the Hartree–Fock framework. Atomic units are usedthroughout.