On the relativistic L-S coupling
  The fact that the Dirac equation is linear in the space and time derivatives leads to the coupling of spin and orbital angular momenta that is of a pure relativistic nature. We illustrate this fact by computing the solutions of the Dirac equation in an infinite spherical well, which allows to go from the relativistic to the non-relativistic limit by just varying the radius of the well. 
P. Alberto, M. Fiolhais and M. Oliveira