In standard QM textbooks, when calculating the spin-orbit interaction term as a relativistic perturbation for hydrogenic atoms, it is said that the term gives 0 contribution for the s-orbitals (l = 0). This is apparently because the term has the form of S*L and L=0 for the s-orbitals. 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.