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

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Farid, M, Abdel-Hady, A, Nasser, I and Farid, Mohsen 2017. Comparative study of the scaling behavior of the Rényi entropy for He-like atoms. IOP Publishing. https://doi.org/10.1088/1742-6596/869/1/012011
AuthorsFarid, M, Abdel-Hady, A, Nasser, I and Farid, Mohsen
Abstract

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.

KeywordsGeneral Physics and Astronomy; Rényi entropy, Fisher entropy, Shannon entropy, scaling behavior, He-like atoms
Year2017
PublisherIOP Publishing
ISSN1742-6588
Digital Object Identifier (DOI)https://doi.org/10.1088/1742-6596/869/1/012011
Web address (URL)http://hdl.handle.net/10545/625279
http://iopscience.iop.org/info/page/text-and-data-mining
hdl:10545/625279
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Publication dates11 Jul 2017
Publication process dates
Deposited23 Oct 2020, 11:32
Accepted01 Mar 2017
JournalJournal of Physics
Journal of Physics: Conference Series
Journal citation869, p. 012011
ContributorsUniversity of Derby, Egyptian Chinese University, Cairo, Egypt and King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
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