Complexity Study of a Single Particle Under q-Deformed Potentials

TL;DR

This paper investigates how the statistical complexity measure varies for a particle in q-deformed potentials, revealing q-dependent behaviors in harmonic oscillator and Morse potential models.

Contribution

It introduces a detailed analysis of the complexity measure for q-deformed quantum systems using Shannon entropy and disequilibrium, highlighting new q-dependent features.

Findings

Complexity shows a minimum at certain q-values for the harmonic oscillator.

Complexity decreases with increasing q for Morse potentials.

Behavior varies across different energy levels and molecular models.

Abstract

We have studied the variation of the position space statistical complexity measure defined by L\'{o}pez-Ruiz, Mancini, and Calbet such as the product of exponential of the Shannon information entropy and the disequilibrium by using the 1D-normalized probability densities derived from solutions of the Schr\"{o}dinger equation corresponding to the q-deformed harmonic oscillator and q-deformed Morse potentials. An analysis of the numerical results in terms of Shannon information entropy, disequilibrium and complexity measure are presented. In q-deformed harmonic oscillator, q-dependence of the complexity shows a minimum point for all excited energy levels. In the case of q-deformed Morse Potential, complexity decreases with increasing $q$ for the investigated diatomic molecules.