Lower Bound for LMC complexity measure

TL;DR

This paper derives a lower bound for the LMC shape complexity measure, providing analytical relations for specific quantum systems and numerical examples, revealing parameter independence in homogeneous potentials.

Contribution

It introduces a new lower bound for the LMC complexity measure and analyzes its behavior across different quantum systems and potentials.

Findings

Lower bound for LMC complexity derived

Analytical relations for harmonic oscillator and hydrogen atom

Parameter independence in homogeneous potentials

Abstract

Lower bound for the shape complexity measure of L\'opez-Ruiz-Mancini-Calbet (LMC), $C_{LMC}$, is derived. Analytical relations for simple examples of the harmonic oscillator, the hydrogen atom and two-electron 'entangled artificial' atom proposed by Moshinsky are derived. Several numerical examples of the spherically confined model systems are presented as the test cases. For the homogeneous potential, $C_{LMC}$ is found to be independent of the parameters in the potential which is not the case for the non-homogeneous potentials.