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

Frontiers in Theoretical and Applied Physics/UAE 2017

Farid, M.^1 ; Abdel-Hady, A.^2 ; Nasser, I.^3

Department of Electronics, Computing and Mathematics, University of Derby, Derby

DE22 1GB, United Kingdom^1

Department of Basic Sciences, Faculty of Engineering, Egyptian Chinese University, Cairo, Egypt^2

Department of Physics, King Fahd University of Petroleum and Minerals, Dhahran

31261, Saudi Arabia^3

关键词: Comparative studies;    Hylleraas coordinates;    Information entropy;    Logarithmic equations;    Scaling behavior;    Scaling procedures;    Variational parameters;    Variational principles;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/869/1/012011/pdf
DOI  :  10.1088/1742-6596/869/1/012011

来源: IOP

【 摘 要 】

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.