Energy spectrum for a short-range 1/r singular potential with a non-orbital barrier using the asymptotic iteration method

TL;DR

This paper calculates the energy spectrum of a novel short-range potential with a 1/r singularity and a non-orbital barrier using the asymptotic iteration method, providing new insights into its quantum properties.

Contribution

First to compute the energy spectrum of this specific potential using the asymptotic iteration method, validating results with Hamiltonian matrix diagonalization.

Findings

Energy spectrum obtained for the potential.

Validation through Hamiltonian matrix diagonalization.

Introduction of a new approach for this potential.

Abstract

Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the "potential parameter spectrum". Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.