I am looking for the del of spherical harmonics. For the laplace operator we have the defining relation: $\Delta Y^l_m = l(l+1) Y^l_m$.
So, what is with: $\nabla Y^l_m $
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Do you know the definitions of $Y^l_m$ and $\nabla$? If you do, try applying the latter to the former, otherwise checking the definitions is the first thing to do. – lisyarus Sep 08 '20 at 11:31
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Yes, but this is a bit of work and I thought there are some relations which I don't know yet. I was looking for something like eq.16 here: https://www.questaal.org/docs/numerics/spherical_harmonics/#gradients-of-spherical-harmonics – nuemlouno Sep 08 '20 at 11:32
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Doesn't this link answer your question? – lisyarus Sep 08 '20 at 14:44