Position and momentum information-theoretic measures of the pseudoharmonic potential

TL;DR

This paper investigates various information-theoretic measures in position and momentum spaces for the pseudoharmonic potential, providing analytical and numerical results applicable to diatomic molecules, and explores how these measures vary with quantum numbers.

Contribution

It presents analytical expressions for Renyi and Tsallis entropies in both spaces using advanced mathematical techniques, and analyzes the behavior of multiple information measures for diatomic molecules.

Findings

Fisher information increases with quantum number n and decreases with angular momentum .

Shannon entropy increases with n and decreases with  in both spaces.

Onicescu information energy values are obtained and ratios of information measures are analyzed.

Abstract

In this study, the information-theoretic measures in both the position and momentum spaces for the pseudoharmonic potential using Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy and Onicescu information energy are investigated analytically and numerically. The results obtained are applied to some diatomic molecules. The Renyi and Tsallis entropies are analytically obtained in position space using Srivastava-Niukkanen linearization formula in terms of the Lauricella hypergeometric function. Also they are obtained in the momentum space in terms of the multivariate Bell polynomials of Combinatorics. We observed that the Fisher information increases with $n$ in both the position and momentum spaces, but decreases with $\ell$ for all the diatomic molecules considered. The Shannon entropy also increases with increasing $n$ in the position space and decreases with increasing $\ell$. The variations of the Renyi and Tsallis entropies with $\ell$ are also discussed. The exact and numerical values of the Onicescu information energy are also obtained, after which the ratio of information-theoretic impetuses to lengths for Fisher, Shannon and Renyi are obtained.