2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172575The Dirac hydrogen atom with spin symmetry is shown has a SO(4) symmetry. The generators are derived, and the corresponding Casimir operator leads to the energy spectrum naturally. This type hydrogen atom is connected to a four-dimensional Dirac system with equal scalar and vector harmonic oscillator potential, by the Kustaanheimo-Stiefel transformation with a constraint.3 pages,Accepted by PRA as a Rapid CommunicationQuantum PhysicsNuclear Theorytext