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

TL;DR

This paper applies the Asymptotic Iteration Method to solve the nonrelativistic wave equation for a new class of infinite one-dimensional wells with non-flat bottoms, providing energy spectra and validating results against existing methods.

Contribution

It introduces a novel application of AIM to a recently proposed potential in quantum wells, expanding the set of exactly solvable models and presenting new energy spectrum results.

Findings

Energy eigenvalues match TRA results for known potentials.

New energy spectrum data for the proposed potential.

Validation of AIM as an effective method for this class of problems.

Abstract

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.