Generalized electromagnetic fields associated with the Coulomb-like atom problem

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 π^- meson, we restate the Klein–Gordon equation for the Coulomb-like problem incorporating a generalized minimal electromagnetic replacement. The corresponding interaction keeps the 1 / | q| dependence in both the scalar potential V(| q|) and the vector potential A(q) (| A(q) | ∼ 1 / | q|). This equation can be exactly solved in closed form. Thus, we present a novel relativistic quantum-mechanical model which can be further explored.