Cr\'amer-Rao complexity of the two-dimensional confined hydrogen

TL;DR

This study analyzes the internal disorder of a two-dimensional confined hydrogen atom using the Crámer-Rao complexity measure, revealing how confinement influences the system's complexity across various quantum states.

Contribution

It introduces the application of the Crámer-Rao complexity measure to the 2D confined hydrogen atom, providing new insights into how confinement affects quantum complexity.

Findings

Confinement affects the variance and Fisher information of the electron distribution.

The Crámer-Rao complexity measure distinguishes system complexity for all quantum states.

Complexity varies with confinement radius in position and momentum spaces.

Abstract

The internal disorder of the two-dimensional confined hydrogenic atom is numerically studied in terms of the confinement radius for the 1\textit{s}, 2\textit{s}, 2\textit{p} and 3\textit{d} quantum states by means of the statistical Cr\'amer-Rao complexity measure. First, the confinement dependence of the variance and the Fisher information of the position and momentum spreading of its electron distribution are computed and discussed. Then, the Cr\'amer-Rao complexity measure (which quantifies the combined balance of the charge concentration around the mean value and the gradient content of the electron distribution) is investigated in position and momentum spaces. We found that confinement does distinguish complexity of the system for all quantum states by means of this two component measure.