Quantization rule solution to the Hulth\'en potential in arbitrary dimension by a new approximate scheme for the centrifugal term

TL;DR

This paper introduces a new systematic approximation scheme to solve the Hulthén potential in arbitrary dimensions, providing accurate bound state energies and wave functions using an improved quantization rule.

Contribution

The paper presents a novel approximation method for the centrifugal term in the Hulthén potential, applicable in any dimension, enhancing solution accuracy for bound states.

Findings

Accurate energy spectra for Hulthén potential in arbitrary dimensions.

Effective approximation scheme for the centrifugal term.

Solutions for three-dimensional and s-wave cases discussed.

Abstract

The bound state energies and wave functions for a particle exposed to the Hulth\'en potential field in the D-dimensional space are obtained within the improved quantization rule for any arbitrary l state. The present approximation scheme used to deal with the centrifugal term in the effective Hulth\'en potential is systematic and accurate. The solutions for the three-dimensional (D=3) case and the s-wave (l=0) case are briefly discussed. Keywords: Hulth\'en potential, improved quantization rule, approximation schemes. 03.65.Ge, 12.39.Jh