# New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

## TL;DR

This paper presents a unified method to find exact bound-state solutions of the D-dimensional Klein-Gordon equation by mapping it onto the nonrelativistic Morse potential, covering various potentials and couplings.

## Contribution

It introduces a novel mapping technique that yields analytical solutions for the Klein-Gordon equation, including special cases like the Klein-Gordon oscillator.

## Key findings

- Eigenfunctions in terms of generalized Laguerre polynomials
- Eigenenergies derived from solutions of irrational equations
- Unified approach encompasses several known analytical results

## Abstract

New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approach