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## Main Question or Discussion Point

Hi,

I refer to the second edition (international edition) of Griffiths. He proves that the total fine structure correction (spin orbital plus relativistic) is given by

[itex]E_{fs}^{1}\propto (3-\frac{4n}{j+1/2})[/itex]

After that, he writes this. "Fine structure breaks the degeneracy in l (that is, for a given n, the different allowed values of l do not all carry the same energy) but preserves the degeneracy in j"

Isn't he mixing up l and j? From the relation, it appears that fine structure correction depends on j and not on l. So for a given n, different j values end up with different corrections while the degenracy in l is preserved. Or have I made a mistake in understanding what he is saying? Thank you.

I refer to the second edition (international edition) of Griffiths. He proves that the total fine structure correction (spin orbital plus relativistic) is given by

[itex]E_{fs}^{1}\propto (3-\frac{4n}{j+1/2})[/itex]

After that, he writes this. "Fine structure breaks the degeneracy in l (that is, for a given n, the different allowed values of l do not all carry the same energy) but preserves the degeneracy in j"

Isn't he mixing up l and j? From the relation, it appears that fine structure correction depends on j and not on l. So for a given n, different j values end up with different corrections while the degenracy in l is preserved. Or have I made a mistake in understanding what he is saying? Thank you.