Numerical Solution of the Schr\"odinger Equation for a Short-Range 1/r Singular Potential with any L Angular Momentum

TL;DR

This paper extends the application of the Asymptotic Iteration Method to solve the Schrödinger equation with a short-range 1/r potential for any angular momentum, providing accurate energy spectra and comparing favorably with other methods.

Contribution

It introduces non-zero angular momentum into the AIM framework for this potential, expanding its applicability and accuracy in quantum mechanical problems.

Findings

Good agreement with PPSM and CSM methods

Accurate energy eigenvalues for various parameters

Extension of AIM to non-zero angular momentum

Abstract

Recently, the Asymptotic Iteration Method (AIM) was used to calculate the energy spectrum for a short rang three parameter central potential which was introduced by H. Bahlouli and A. D. Alhaidari. The S-orbital wave solution of the Schr\"odinger equation was obtained for different parameters of the potential. In this work a non-zero angular momentum term were introduced to the problem and the energy eigenvalues were obtained for different potential parameters. Our results show very good agreements compared with other methods such as potential parameter spectrum method (PPSM) and the complex scaling method (CSM).