Fine structure correction in H atom

[McLaren Rulez]

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

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

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.

 

[McLaren Rulez]

So anybody knows if this is a typo in the text or if I've got it wrong? Thank you

 

[florence webber]

So anybody knows if this is a typo in the text or if I've got it wrong? Thank you

interestingly enough (or not!) in the 1995 edition page 242 the text reads:

".... 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); the energies are determined by n and j (see Figure 6.9)...."

which maybe makes a bit more sense!