Using the AIM for solving the non-relativistic wave equation for a new class of infinite one-dimensional well with non-flat bottom

Abstract

The main goal of this work is to solve the non-relativistic wave equation for a new potential configuration that describes the quantum states of a particle that lies within a one-dimensional 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 together with new results for the energy spectrum have been presented.