Using the AIM for solving the nonrelativistic wave equation for new class of infinite one dimensional well with none flat bottom

The main goal of this work is to solve the nonrelativistic wave equation for a new potential configuration that describes the quantum states of a particle that lies within a onedimensional infinite well of width L using the Asymptotic Iteration Method (AIM). This potential was introduced recently by Alhaidari to be added to the class of exactly solvable potentials in the Tridiagonal Representation Approach (TRA). We have obtained the energy eigenvalues for different choices of the potential parameters. A good match between our results and the ones obtained by the TRA are shown in Table 1. Moreover, new results have been presented in Table 2 and Table 3 for the energy spectrum.