Generalized statistical complexity and Fisher-Renyi entropy product in the $H$-atom

Details Generalized statistical complexity and Fisher-Renyi entropy product in the $H$-atom Generalized statistical complexity and Fisher-Renyi entropy product in the $H$-atom

2009-01-13

arxiv.org/abs/0901.1752v1

Nonlinear Sciences

Pattern Formation and Solitons

10 pages, 3 figures

Scientific paper

By using the Renyi entropy, and following the same scheme that in the Fisher-Renyi entropy product case, a generalized statistical complexity is defined. Several properties of it, including inequalities and lower and upper bounds are derived. The hydrogen atom is used as a test system where to quantify these two different statistical magnitudes, the Fisher-Renyi entropy product and the generalized statistical complexity. For each level of energy, both indicators take their minimum values on the orbitals that correspond to the highest orbital angular momentum. Hence, in the same way as happens with the Fisher-Shannon and the statistical complexity, these generalized Renyi-like statistical magnitudes break the energy degeneration in the H-atom.

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