1. In class we derived selection rules for transitions between electronic states of the hydrogen atom. In doing so, we used a little known known rule for the value of an integral containing three spherical harmonic functions. Here we will show that the nules flow directly from the properties of () and v() that combine to form the spherical harmonics. The important point that we will deal with in detail in Chem 113C, is for all allowed transitions the transition dipole moment integral must be none-zero. That is: ro=rf(r)^ff(r)dr=0 Where ^=er^=e(x^+y^+z^)x^=rsin()cos()m=1,2,y^=rsin()sin()2^=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: f which will depend on the integral m which will depend on the integral a) We will start with the l quantum number ()im=NtmPm2()=cos() The legendre polynomials P1=have a rocursion relationship cos()Ptm=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