Ro-vibrational energy analysis of Manning–Rosen and Pöschl–Teller potentials with a new improved approximation in the centrifugal term

Two physically important potentials (Manning-Rosen and P\"oschl-Teller) are considered for the ro-vibrational energy in diatomic molecules. An improved new approximation is invoked centrifugal term, which then used their solution within Nikiforov-Uvarov framework. This employs a recently proposed scheme, combines two widely Greene-Aldrich Pekeris-type approximations. Thus, approximate analytical expressions derived eigenvalues eigenfunctions. The energies examined with respect to parameters, $\lambda$ $\nu$. original approximations recovered certain specials values of these parameters. offers simple effective scheme other relevant quantum mechanics.