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Title: Entropy and complexity analysis of hydrogenic Rydberg atoms

The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following information-theoretic spreading quantities: the radial and logarithmic expectation values, the Shannon entropy, and the Fisher information. As well, the complexity measures of Cramer-Rao, Fisher-Shannon, and Lopez Ruiz-Mancini-Calvet types are investigated in both reciprocal spaces. The leading term of these quantities is rigorously calculated by use of the asymptotic properties of the concomitant entropic functionals of the Laguerre and Gegenbauer orthogonal polynomials which control the wavefunctions of the Rydberg states in both position and momentum spaces. The associated generalized Heisenberg-like, logarithmic and entropic uncertainty relations are also given. Finally, application to linear (l= 0), circular (l=n- 1), and quasicircular (l=n- 2) states is explicitly done.
Authors:
 [1] ;  [2] ; ;  [1] ;  [2] ;  [1] ;  [2]
  1. Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071-Granada (Spain)
  2. (Spain)
Publication Date:
OSTI Identifier:
22163004
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 5; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ASYMPTOTIC SOLUTIONS; ATOMS; DENSITY; ENTROPY; EXPECTATION VALUE; HYDROGEN; POLYNOMIALS; PROBABILITY; RYDBERG STATES; WAVE FUNCTIONS