The Klein-Gordon equation with the Kratzer potential in d dimensions

TL;DR

This paper uses the Asymptotic Iteration Method to find exact bound-state energy spectra for the Klein-Gordon equation with various potentials in multiple dimensions, including Coulombic and Kratzer types.

Contribution

It provides exact solutions for the Klein-Gordon equation with scalar and vector potentials of Coulombic and Kratzer types in d dimensions, extending previous methods.

Findings

Exact solutions for Coulombic potentials in all cases.

Exact solutions for Kratzer potentials when S(r)=V(r).

General solutions involving elementary symmetric polynomials.

Abstract

We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r)=V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.