We have studied the spin orbit-coupling from the Dirac equation, Understanding thernproperties of electronic states in quantum wires is a central issue in nanoscience. Inrnthe ballistic region, with low electronic densities, electron-electron interactions are notrnvery important, and wire conductance is determined by the transmission of electronsrnas independent particles and the effects of spin-orbit interaction (SOI) on the energyrnbands,a system of two dimensional equations with respect to the spinor componentsrn "#(t), in the case of = 0, 6= 0 and ballistic conductance