Consider the action of an infinitesimal rotation about the n axis of an angular momentum eigenstate nm.

Consider the action of an infinitesimal rotation about the n axis of an angular momentum eigenstate Ψnℓm. Show that

and find the complex numbers D_m'm (they will depend on δ, n, and ℓ as well as m and m'). This result makes sense: a rotation doesn’t change the magnitude of the angular momentum (specified by ℓ) but does change its projection along the z axis (specified by m).

Transcribed Image Text:

Rn (8) Vnem Dm'mnem', m'