  Using the relativistic quantum stationary Hamilton-Jacobi equation within the
framework of the equivalence postulate, and grounding oneself on both
relativistic and quantum Lagrangians, we construct a Lagrangian of a
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 plot the relativistic quantum trajectories of a particle moving
under the constant and the linear potentials. We establish the existence of
nodes and link them to the de Broglie's wavelength.
