Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

In this study, we present the analytical solutions of bound states for the Schrödinger equation with the multiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeris-type approximation to the centrifugal potential. For any n and l (states) quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues. Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.