Study of a confined Hydrogen-like atom by the Asymptotic Iteration Method

TL;DR

This paper applies the asymptotic iteration method to analyze a confined hydrogen-like atom, providing exact and approximate solutions, and determining critical confinement radii where bound states vanish.

Contribution

It introduces AIM for solving confined atomic systems, offering new analytical and numerical insights into bound states and critical radii.

Findings

Calculated critical box radii for bound state disappearance

Obtained exact solutions for specific cases

Provided approximate solutions validated against literature

Abstract

The asymptotic iteration method (AIM) is used to obtain both special exact solutions and general approximate solutions for a Hydrogen-like atom confined in a spherical box of arbitrary radius R. Critical box radii, at which states are no longer bound, are also calculated. The results are compared with those in the literature.