Find the commutators of the spherical operators \(a_{0, \pm 1}^{\dagger}\) defined in Eq. (11.23) with the angular momentum operators. Thus show that they transform as rank-1 spherical tensors under SO(3).

Data from Eq. 11.23

Transcribed Image Text:

1 =(ax iay) do = az a = (a (a ia) a = a 2 = 1p