Entropy and complexity analysis of hydrogenic Rydberg atoms

Journal Article · Wed May 15 00:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4807095· OSTI ID:22163004

Lopez-Rosa, S. ^[1]; Toranzo, I. V.; Dehesa, J. S. ^[1]; Sanchez-Moreno, P. ^[1]

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1. Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071-Granada (Spain)

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.

• OSTI ID: 22163004
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 5; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ASYMPTOTIC SOLUTIONS
ATOMS
DENSITY
ENTROPY
EXPECTATION VALUE
HYDROGEN
POLYNOMIALS
PROBABILITY
RYDBERG STATES
WAVE FUNCTIONS