where ‖ ‖ λ λ ‖ ‖ = λ λ ( λ λ + 1 ) ℏ ℏ , and its z-projection is given by λ λ z = μ μ ℏ ℏ ; and where J i and J f are, respectively, the initial and final angular momenta of the atom. The corresponding quantum numbers λ and μ (z -axis angular momentum) must satisfy