Eur. Phys. J. Plus (2020) 135: 220
https://doi.org/10.1140/epjp/s13360-020-00244-8

Regular Article

Generalized electromagnetic fields associated with the Coulomb-like atom problem

¹ Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de Los Andes, Santiago, Chile
² Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Concepcion, Concepcíon, Chile

^* e-mail: jdiaz@udec.cl

Received: 10 July 2019
Accepted: 22 January 2020
Published online: 4 February 2020

Abstract

It is well known that the principle of minimal coupling in quantum mechanics establishes a unique interaction form for a charged particle. By properly redefining the canonical commutation relations between (canonical) conjugate components of position and momentum of the particle, e.g., a meson, we restate the Klein–Gordon equation for the Coulomb-like problem incorporating a generalized minimal electromagnetic replacement. The corresponding interaction keeps the dependence in both the scalar potential and the vector potential . This equation can be exactly solved in closed form. Thus, we present a novel relativistic quantum-mechanical model which can be further explored.