A vector operator has spherical components ( ) obeying
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin
Deriving the Spectrum, Ch Fine structure and the Lamb shift
Problem
A vector operator V has spherical components Vq (q=0,±1) obeying, between levels of definite total angular momentum, ⟨j′m′∣Vq∣jm⟩=0 unless m′=m+q and j′=j,j±1 (never j=0→j′=0).
((a)) Decide whether some component of V can connect the state ∣j=2,m=1⟩ to ∣j′=1,m′=0⟩, and if so say which component Vq it is.
((b)) Decide whether any component of V can connect ∣j=2,m=1⟩ to ∣j′=0,m′=1⟩.