The Effects of Non-linearity on the Solutions of Manning-Rosen and Hulthén Three-Dimensional Potentials Using Quantum Supersymmetry and N–U Methods: Application to CO\(^\mathbf{+}\), BO and CN Diatomic Molecules

Abstract

The three-dimensional Schrödinger equation, where a non-linearity is caused by the introduction of an energy-dependent potential, is solved in the case of Energy-Dependent Manning-Rosen Potential (EDMRP) by means of extended quantum supersymmetry (EQS) combined with shape invariance, and Nikiforov–Uvarov (N–U) methods, using in both cases the Pekeris approximation for the centrifugal term. On the one hand, after determining the potential parameters according to experimental data, EQS and N–U results are compared to the numerical ones to show the effectiveness of our calculations. On the other hand, the effects of the non-linearity introduced via energy-dependent potentials in the Schrödinger equation are shown through a comparison made between energy-dependent and position-only-dependent cases of the Manning-Rosen potential. We considered some diatomic molecules CO\(^{+}\), BO, and CN with the experimental values of their potential parameters. Our results allowed us to consider, as a particular case, the three-dimensional energy-dependent Hulthén potential.