Hi, this is probably a stupid question, but I suck at maths
in a problem sheet for atomic physics I've been told to use:
the integral of Y*_lm Y_l'm' sin(theta) dthetadphi = kronecker delta_l,l' kronecker delta m,m'
I get that kronecker delta of l,m = 1 if theyre equal, 0 otherwise, but I don't understand what the subscripts mean in this case, how are l,m related to l prime and m prime?
In my question I have a sum over a (from 0 to infinity), and a sum over b (from -a to a) of Y*_ab(theta1,phi1) Y_ab(theta2,phi2) which I'm then integrating over two volumes, dV_1,dV_2. (theres some other stuff as well, that depends on r1 and r2) How do I rewrite this Y*Y part in terms of delta functions? It would be nice if that whole part was just delta_ab but I can't just write that down.
*edit* this is what I have to work out: