  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.
