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The well-known trigonometric Scarf potential is generalized by adding asinusoidal term and then treated using the Asymptotic Iteration Method (AIM)and the Tridiagonal Representation Approach (TRA). The energy spectrum of theassociated bound states are computed. For the AIM, we have improved convergenceof the quantization condition that terminates the iterations asymptotically.This is accomplished by looking for the range of initial values of the spacevariable in the terminating condition that produces stable results (plateau ofconvergence). We have shown that with increasing iteration this plateau ofconvergence grows up rapidly to an optimal iteration number and then shrinksslowly to a point. The value of this point (or points) may depend on thephysical parameters. The numerical results have been compared favorably withthose resulting from the TRA.

Energy spectrum of a generalized Scarf potential using the Asymptotic Iteration Method and the Tridiagonal Representation Approach