TD=rf(r)^f(r)d0 Where ^=er^=e(x^+y^+z^)x^=rsin()cos()y^=rsin()sin()}m=1,2,z^=rcos()m=0 We noted that the integral over r is always none-zero, so the selection rules depend on the and integrals. There are two quantum numbers we are concerned with: l which will depend on the integral m which will depend on the integral a) We will start with the l quantum number ()lm=NlmPlmz^()=cos() The legendre polynomials Plm have a recursion relationship cos()Plm=2l+11[(lm+1)Pl+1m+(l+m)Pl1m] Use this relationship and the fact the wavefunctions generated from these polynomials are orthogonal to show that l=1