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However this S*L is preceded by a factor proportional to 1/r^3 and the expectation value of 1/r^3 for the l=0 states gives ∞.

So I think, strictly speaking, when one evaluates the 1st order perturbation caused by the spin-orbit coupling for the s-orbital states, one has to deal with ∞*0 and I guess it gives a finite contribution.

But as far as I can see, I've never seen any textbooks/articles arguing this subtlety.

Am I wrong or missing something?

Any comments are welcome.

Thanks.