When the orbital angular momentum and spin angular momentum are coupled, the total angular momentum is of the general form for quantized angular momentum
where the total angular momentum quantum number is
This gives a z-component of angular momentum
This kind of coupling gives an even number of angular momentum levels, which is consistent with the multiplets seen in anomalous Zeeman effects such as that of sodium.
As long as external interactions are not extremely strong, the total angular momentum of an electron can be considered to be conserved and j is said to be a "good quantum number". This quantum number is used to characterize the splitting of atomic energy levels, such as the spin-orbit splitting which leads to the sodium doublet.
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