Exact solutions of Klein Gordon equation for the Makarov potential with the asymptotic iteration method

TL;DR

This paper derives exact analytical solutions for the Klein-Gordon equation with the Makarov potential using the asymptotic iteration method, providing explicit energy eigenvalues and eigenfunctions.

Contribution

It introduces a novel application of the asymptotic iteration method to solve the Klein-Gordon equation with the Makarov potential, yielding closed-form solutions.

Findings

Closed-form energy eigenvalues obtained

Normalized eigenfunctions expressed in special functions

Method demonstrates effectiveness for this potential

Abstract

We derive exact analytical solutions of the Klein-Gordon equation for Makarov potential by means of the asymptotic iteration method. The energy eigenvalues are given in a closed form and the corresponding normalized eigenfunctions are obtained in terms of the generalized Laguerre polynomials and hypergeometrical functions.