Eur. Phys. J. Plus (2021) 136: 612
https://doi.org/10.1140/epjp/s13360-021-01602-w

Regular Article

Quaternionic Klein–Gordon equation

Departamento de Matemática Pura e Aplicada, Universidade Federal do Rio Grande do Sul (UFRGS), Caixa Postal 15080, Avenida Bento Gonçalves 9500, 91501-970, Porto Alegre, RS, Brazil

^a sergio.giardino@ufrgs.br

Received: 17 January 2021
Accepted: 23 May 2021
Published online: 1 June 2021

Abstract

We solve Klein–Gordon equation (KGE) in the framework of the real Hilbert space approach to quaternionic quantum mechanics ($\mathbb{H}\text{QM}$). The presented solution is the simplest ever obtained for quaternionic quantum theories and the closest to the complex solution. The scattering of a quaternionic charged scalar particle from an electric field is also obtained. A remarkable feature of quaternionic scalar particles is the existence of massive light cone particles.