Eigensolution techniques, their applications and the Fisher's information entropy of Tietz-Wei diatomic molecular model

TL;DR

This paper develops approximate analytical solutions for quantum wave equations under the Tietz-Wei diatomic potential using three eigensolution techniques, compares their results, and analyzes the Fisher's information entropy of the system.

Contribution

It introduces a unified approach applying FAA, SUSYQM, and AIM to solve quantum equations for the Tietz-Wei potential, demonstrating their equivalence and analyzing quantum information measures.

Findings

All three methods yield identical energy eigenvalues and eigenfunctions.

The Fisher's information entropy provides insights into quantum states of the diatomic potential.

Numerical results and probability distributions are characterized by Jacobi polynomials.

Abstract

In this study, approximate analytical solution of Schr\"odinger, Klein-Gordon and Dirac equations under the Tietz-Wei (TW) diatomic molecular potential are represented by using an approximation for the centrifugal term. We have applied three types of eigensolution techniques; the functional analysis approach (FAA), supersymmetry quantum mechanics (SUSYQM) and asymptotic iteration method (AIM) to solve Klein-Gordon Dirac and Schr\"odinger equations, respectively. The energy eigenvalues and the corresponding eigenfunctions for these three wave equations are obtained and some numerical results and figures are reported. It has been shown that these techniques yielded exactly same results. some expectation values of the TW diatomic molecular potential within the framework of the Hellmann-Feynman theorem (HFT) have been presented. The probability distributions which characterize the quantum-mechanical states of TW diatomic molecular potential are analysed by means of complementary information measures of a probability distribution called the Fishers information entropy. This distribution has been described in terms of Jacobi polynomials, whose characteristics are controlled by the quantum numbers.