Systematics of eigenstates

The nonrelativistic limit of (116) is easily computed. We subtract the rest-mass rrK from the energy, that is, we write 

Hence we see that for the Coulomb problem in the Schrbdinger equation, the eigenvalue depends only on the principal quantum number  

So there is a much higher degeneracy in the nonrelativistic limit. 

As there is a one to one correspondence between the relativistic eigenstates and their nonrelativistic limit, the spectroscopic notation (which uses nonrelativistic quantum numbers ) can also be used to label the relativistic states. Hence the eigenstates of h. can be denoted as follows  

The spectroscopic notation does not distinguish between states that belong to different eigenvalues nij of Jz- Hence the state Nxj has the multiplicity 2j -t-1. 

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