The exact fine-structure formula for hydrogen (obtained from the dirac equation without ecourse to perturbation theory) is: 21-1/2 enj mc 5+1/2)2 - a2 n - (j1/2) expand to order a4 (noting that a < < 1), and show that you recover: 13.6ev 3 enj 1+ n2 j+1/2 a handy relation, not necessarily needed for the exercises: e1 (6) mc2