Question

calculate the angles which the angular momentum vector forms with the z-axis in some 3 states of a particle on a sphere described by spherical harmonics Y_2,2, Y_2,-1, Y_2-0

Answer 1

Y_2,2 = (15/32 $\pi$ )^1/2 sin² $\Theta$ e^{-2i $\Phi$}

Y_2,-1 = (15/8 $\pi$ )^1/2 cos $\Theta$ sin $\Theta$ e^{i $\Phi$}

Y2,0 = (5/16 $\pi$ )^1/2 (3cos² $\Theta$ - 1)