Complexity of D-dimensional hydrogenic systems in position and momentum spaces

S. López-Rosa, D. Manzano and J.S. Dehesa

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 15, 3273-3281

Abstract: The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal spaces. This quantity, which is the product of the disequilibrium or averaging density and the Shannon entropic power, is mathematically expressed for both ground and excited stationary states in terms of certain entropic functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. We emphasize the ground and circular states, where the complexity is explicitly calculated and discussed by means of the quantum numbers and dimensionality. Finally, the position and momentum shape complexities are numerically discussed for various physical states and dimensionalities, and the dimensional and Rydberg energy limits as well as their associated uncertainty products are explicitly given. As a byproduct, it is shown that the shape complexity of the system in a stationary state does not depend on the strength of the Coulomb potential involved.

Keywords: Hydrogenic systems; Information theory; D-dimensional physics; Shannon entropy; Shape complexity; Disequilibrium (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:15:p:3273-3281

DOI: 10.1016/j.physa.2009.04.023

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