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