2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230551Within CPT-symmetric quantum mechanics the most elementary differential form of the charge operator C is assumed. A closed-form integrability of the related coupled differential self-consistency conditions and a natural embedding of the Hamiltonians in a supersymmetric scheme is achieved. For a particular choice of the interactions the rigorous mathematical consistency of the construction is scrutinized suggesting that quantum systems with non-self-adjoint Hamiltonians may admit probabilistic interpretation even in presence of a manifest breakdown of both T symmetry (i.e., Hermiticity) and PT symmetry.13 pagesMathematical Physics46C50; 81Q60; 81P10; 81S99; 81Q05text