Exact Hamiltonian for an analytic correlated ground-state wave function for He-like ions

A correlated three-parameter variational ground-state Ψ(r1,r2,r12) proposed by Chandrasekhar for helium-like ions gives a high percentage of the electron correlation energy resulting from the interaction energy e2/r12 and also yields an analytic ground-state electron density ρ(r). Here, we extract via Schrödinger equation an exact Hamiltonian for which the Chandrasekhar wave function is the ground-state. Properties of the potential energy function in this Hamiltonian are quantified. Finally, kinetic energy densities are plotted and related to the Laplacian of ρ(r).