The continuity equation and its applications in phase space quantum mechanics

A quantum phase space version of the continuity equation for systems with internal degrees of freedom is derived. The $1$ – D Dirac equation is introduced and its phase space counterpart is found. The phase space representation of free motion and of scattering in a nonrelativistic and relativistic case for setups with internal degrees of freedom is discussed and illustrated. Properties of Wigner functions of unbound states are analysed.