Rényi, Shannon and Tsallis entropies of Rydberg hydrogenic systems
Abstract
The Rényi entropies R_{p}[ρ], 0 of the probability density ρ_{n,l,m}(r ) of a physical system completely characterize the chemical and physical properties of the quantum state described by the three integer quantum numbers (n,l,m) . The analytical determination of these quantities is practically impossible up until now, even for the very few systems where their Schrödinger equation is exactly solved. In this work, the Rényi entropies of Rydberg (highly excited) hydrogenic states are explicitly calculated in terms of the quantum numbers and the parameter p. To do that we use a methodology which first connects these quantities to the L_{p} norms N_{n,l}(p) of the Laguerre polynomials which characterize the state's wave function. Then, the Rényi, Shannon and Tsallis entropies of the Rydberg states are determined by calculating the asymptotics (n→∞) of these Laguerre norms. Finally, these quantities are numerically examined in terms of the quantum numbers and the nuclear charge.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 February 2016
 DOI:
 10.1209/02955075/113/48003
 arXiv:
 arXiv:1603.09494
 Bibcode:
 2016EL....11348003T
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 Eur. Phys. Lett. (EPL) 113 (2016) 48003