Eigensolution techniques, their applications and Fisherʼs information entropy of the Tietz–Wei diatomic molecular model

Abstract

In this study, the approximate analytical solutions of Schrödinger, 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, supersymmetry quantum mechanics and the asymptotic iteration method to solve the Klein–Gordon, Dirac and Schrödinger 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 the same results. some expectation values of the TW diatomic molecular potential within the framework of the Hellmann–Feynman theorem have been presented. The probability distributions that characterize the quantum mechanical states of TW diatomic molecular potential are analyzed by means of complementary information measures of a probability distribution called Fisherʼs information entropy. This distribution has been described in terms of Jacobi polynomials, whose characteristics are controlled by quantum numbers.