Asymptotic Iteration Solution for Two Novel Hyperbolic Potentials

In this work, we compute the bound states associated with two newly proposed one-dimensional hyperbolic potentials using the asymptotic iteration method (AIM). We find the energy spectrum associated with each potential for a variety of choices of the potential parameters which in their turn affect strongly the potential shape. To confirm the validity of our results we have used two alternative independent numerical schemes, the Lagrange–Hermite mesh and the eight-point finite difference methods, to double check the accuracy of our results. We found an excellent agreement between the results generated by the above three independent numerical methods and existing literature.