2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91577For one dimensional motions, we derive from the Dirac Spinors Equation (DSE) the Quantum Stationary Hamilton-Jacobi Equation for particles with spin 1/2. Then, We give its solution. We demonstrate that the $QSHJES_{1\over2}$ have two explicit forms, which represent the two possible projection of the Spin 1/2.Latex, 8 pages, no figureQuantum PhysicsHigh Energy Physics - Theorytext