Spin symmetry in the relativistic symmetrical well potential including a proper approximation to the spin-orbit coupling term

In the case of exact spin symmetry, we approximately solve the Dirac equation with scalar and vector symmetrical well potentials by using a proper approximation to the spin-orbit coupling term, and obtain the corresponding energy equation and spinor wave functions for the bound states. We find that there exist only positive-energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter alpha goes to zero. The special case for equally scalar and vector symmetrical well potentials is studied briefly.