Comparative study of the scaling behavior of the Rényi entropy for He-like atoms

We solve the Schrödinger equation in the spherical or Hylleraas-coordinate systems, and within the framework of the Ritz's variational principle. The eigenvalues, and the eigenfunctions ψ(r) in r- or Hylleraas-space for the 1s²-state of the He-like atoms as a function of two variational parameters are calculated. Using a simple scaling procedure, we calculate the scaled wavefunction as a function of the nuclear charge Z. Given the density of states, ρ(r), the scaling behavior of the information entropies, e.g., Fisher, Shannon and Rényi's entropies, with their powers and products, as functions of Z are calculated. Scaled wavefunctions for the 1s²-state of the He-like atoms, with exchange, have been used to study the scaling behavior. Our results agree with the published results. Furthermore, we present a simple logarithmic equation that shows the dependence of information entropies on Z for He-like atoms. The formulation enhances the computational efficiency of the entropies and other related quantities.