With the particle-number density identified with \rho= \psi^\dagger\psi, and for a near plane-wave solution of finite extent, we can interpret the first term in the decomposition as the current {\mathbf j}_{\rm free}= e\rho {\mathbf k}/E= e\rho {\mathbf v} due to particles moving at speed {\mathbf v}={\mathbf k}/E.
where |{\mathbf S}|=\hbar/2 and g=2 is the Dirac value of the gyromagnetic ratio.