Inhomogeneous Electron Liquid: H Atom Dirac Density Matrix in Limit of Infinite Number of Closed Shells

Abstract

The Dirac density matrix ρ _N () for the H atom with N closed shells is here treated in the limit N tends to infinity. Then ρ_α () is shown to be derivable exactly from the zero energy limit of the bound state only Green function G_b ^(Z) (; E). It is further demonstrated for nuclear charge Ze that the Laplace transform of G_b ^(Z) with respect to Z satisfies a useful equation of motion. Finally the s-wave only components of ρ_N and G_b ^(Z) are considered.

Key Words:

• Electron liquid
• density matrix
• bound-state Green function