2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89856Using the relativistic quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding one self on both relativistic and quantum Lagrangians, we construct a Lagrangian of relativistic quantum system in one dimension and derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. Then, we investigate the free particle case and establish the photon's trajectories.LaTex, 13 pages, no figures, title changed, minor changesQuantum Physicstext