Due to the spin-orbit interaction, the energies of states of the same level but with different j will no longer be identical. This is because in the original quantum numbers, when is parallel to , the interaction energy is positive, and in this case j = l + s = l + . When is anti-parallel to (i.e. aligned oppositely), the interaction energy is negative, and in this case . Furthermore, the strength of the interaction is roughly proportional to l.

For example, consider the states at level 4:
* The 10 states with j = come from