Rényi, Shannon and Tsallis entropies of Rydberg hydrogenic systems

@article{Toranzo2016RnyiSA,
  title={R{\'e}nyi, Shannon and Tsallis entropies of Rydberg hydrogenic systems},
  author={Irene Valero Toranzo and Jes{\'u}s S. Dehesa},
  journal={EPL},
  year={2016},
  volume={113},
  pages={48003}
}
The Renyi entropies of the probability density of a physical system completely characterize the chemical and physical properties of the quantum state described by the three integer quantum numbers . The analytical determination of these quantities is practically impossible up until now, even for the very few systems where their Schrodinger equation is exactly solved. In this work, the Renyi entropies of Rydberg (highly excited) hydrogenic states are explicitly calculated in terms of the quantum… 
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References

SHOWING 1-6 OF 6 REFERENCES
Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states
The analytic information theory of quantum systems includes the exact determination of their spatial extension or multidimensional spreading in both position and momentum spaces by means of the
Rényi Entropy, Tsallis Entropy and Onicescu Information Energy in Density Functional Reactivity Theory
Density functional theory dictates that the electron density determines everything in a molecular system's ground state, including its structure and reactivity properties. However, little is known
Quantal Information Entropies for Atoms
The polynomials occurring in the wave functionsof hydrogenic excited states are found to presentdifficulties for a straightforward analytical approachto the study of associated information entropies.
The Fisher information of single-particle systems with a central potential
Abstract The Fisher information of single-particle systems with a central potential, which is a gradient functional of their quantum-mechanical probability density, is studied in detail in the
Reviews of modern quantum chemistry : a celebration of the contributions of Robert G. Parr
A collection of state-of-the-art reviews of diverse topics covering almost all the major areas of modern quantum chemistry. The current focus in the discipline of chemistry - synthesis, structure,
Orthogonal Polynomials
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.