Multidimensional hydrogenic complexity

TL;DR

This paper investigates the internal disorder of D-dimensional hydrogenic systems using shape complexity in reciprocal spaces, expressed through entropic functionals of special polynomials, focusing on ground and excited states.

Contribution

It provides a mathematical formulation of shape complexity for hydrogenic systems in multiple dimensions using entropic measures and polynomial functionals, emphasizing ground and circular states.

Findings

Shape complexity is expressed via entropic functionals of Laguerre and Gegenbauer polynomials.

The study focuses on ground and circular states of hydrogenic systems.

Mathematical expressions are derived for both stationary states.

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 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. Emphasis is made in the ground and circular states.