Analysis of quantum-mechanical states of the Mie-type ring shaped model via the Fisher's information entropy

TL;DR

This paper investigates the quantum states of a Mie-type ring-shaped molecular potential using Fisher's information entropy, providing insights into the probability distributions and internal structure of diatomic molecules.

Contribution

It presents analytical solutions for the radial Schrödinger equation with Mie-type potential and analyzes the probability distributions using Fisher's information entropy.

Findings

Derived probability density functions for specific diatomic molecules.

Analyzed Fisher's information entropy to understand quantum state structures.

Provided insights into the internal quantum structure of ring-shaped molecular systems.

Abstract

In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is the strongest support of the modern quantum computation and information, which is basic for numerous technological developments. This study report the any $\ell-$state solution of the radial Schr\"{o}dinger equation with the Mie-type ring shaped diatomic molecular potential. Rotational-vibration of some few selected diatomic molecules are given. The probability distribution density of the system which gives the probability density for observing the electron in the state characterized by the quantum numbers $(n, l, m)$ in the Mie-type ring shaped diatomic molecular potential is obtained. Finally, we analyze this distribution via a complementary information measures of a probability distribution called as the Fisher's information entropy.