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Bill_K is offline
Jul5-11, 06:10 PM
Sci Advisor
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P: 3,853
Spherical harmonics are related to ORBITAL angular momentum, and not to the SPIN angular momentum.
Spin spherical harmonics are related to TOTAL angular momentum. They are eigenfunctions of J, Jz and L, defined as sums of products of orbital and spin wavefunctions:

Ψjℓm(θ,φ) = ∑ (ℓ m μ | ℓ j m) Yℓm(θ,φ) χμ

where ( ... | ) are Clebsch-Gordan coefficients and χμ, μ = are spin states.