Table 2.

Vector spherical harmonics: Polarization character and eigenvalues of J ², J _z, Π, and L ².

	J 2	J z	Π	L 2	Polarization
${\mathbf{Y}}_{j,j,m}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$	j(j + 1)	m	(−1)j + 1	j(j + 1)	⊥
${\mathbf{Y}}_{j,j-\mathrm{1,}m}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$	j(j + 1)	m	(−1)j	(j−1)j	mixed
${\mathbf{Y}}_{j,j+\mathrm{1,}m}(\stackrel{\mathbf{ˆ}}{\mathbf{p}})$	j(j + 1)	m	(−1)j	(j + 1) (j + 2)	mixed

L ² is the orbital angular momentum squared. Both j ≥ 0 and $m=-j\dots j$ are integers. For j = 0, ${\mathbf{Y}}_{0,1,0}=-\stackrel{\mathbf{ˆ}}{\mathbf{p}}/(4\pi )$, Y _0,0,0 = 0, and Y _0,−1,0 is not defined.