Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom

TL;DR

This paper investigates the Fisher-Shannon information and statistical complexity of the hydrogen atom's wave functions, revealing that these measures are minimized at classical Bohr orbits with highest angular momentum.

Contribution

It introduces a novel analysis linking statistical measures to classical Bohr orbits in the hydrogen atom.

Findings

Fisher-Shannon information is minimized at classical circular orbits.

Statistical complexity reaches its lowest values at these orbits.

Results connect quantum wave functions with classical orbital properties.

Abstract

The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the H-atom. For each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the classical (circular) orbits in the Bohr atomic model, just those with the highest orbital angular momentum.