Some features of the statistical complexity, Fisher-Shannon information, and Bohr-like orbits in the Quantum Isotropic Harmonic Oscillator

TL;DR

This paper investigates statistical complexity and Fisher-Shannon information in the quantum isotropic harmonic oscillator, revealing their independence from potential strength and their minimization on classical-like circular orbits with high angular momentum.

Contribution

It demonstrates that these information measures are invariant to potential strength and identifies their minima on classical-like orbits in quantum states.

Findings

Fisher-Shannon information and complexity are independent of potential strength.

These measures are minimized on classical circular orbits with high angular momentum.

The results connect quantum information measures with classical orbital characteristics.

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 quantum isotropic harmonic oscillator. We show that these magnitudes are independent of the strength of the harmonic potential. Moreover, 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-like quantum image, just those with the highest orbital angular momentum.