"Angular momentum 4" Lx(f) = i hbar (sin(phi) d(f,theta) + cos(theta) cos(phi) / sin(theta) d(f,phi)) Ly(f) = i hbar (-cos(phi) d(f,theta) + cos(theta) sin(phi) / sin(theta) d(f,phi)) Lz(f) = -i hbar d(f,phi) LL(f) = -hbar^2 (d(f,theta,theta) + cos(theta) / sin(theta) d(f,theta) + d(f,phi,phi) / sin(theta)^2) Y(l,m) = (-1)^m sqrt((2 l + 1) / (4 pi) (l - m)! / (l + m)!) * P(l,m) exp(i m phi) P(l,m,k) = test(m < 0, (-1)^m (l + m)! / (l - m)! P(l,-m), (sin(theta)/2)^m sum(k, 0, l - m, (-1)^k (l + m + k)! / (l - m - k)! / (m + k)! / k! * ((1 - cos(theta)) / 2)^k)) "Verify eigenfunctions" for(l,0,2, for(m,-l,l, do( psi = Y(l,m), check(LL(psi) = l (l + 1) hbar^2 psi), check(Lz(psi) = m hbar psi) ))) "ok" Run