wigner 9j · recoupling

a⁻ a⁺ b⁻ b⁺ c⁻ c⁺ j₁ j₂ j₃ k₁ k₂ k₃ l₁ l₂ l₃
j₁5.0
5.0
j₂5.0
5.0
j₃5.0
5.0
k₁5.0
5.0
k₂5.0
5.0
k₃5.0
5.0
l₁5.0
5.0
l₂5.0
5.0
l₃5.0
5.0
9j symbol 0.0000 (zero) ⚪ zero
9j = sum over x of (-1)^{2x} (2x+1) * { j₁ j₂ j₃ ; k₁ k₂ k₃ ; l₁ l₂ l₃ } (racah sum over 6j symbols)
what does 9j mean? it appears in the quantum mechanics of angular momentum when three angular momenta are coupled in two different ways. the 9j symbol is the recoupling coefficient between the (j₁,j₂,j₃) and (k₁,k₂,k₃) schemes. it is used in the theory of spectroscopic line strengths, in nuclear and atomic physics, and in the description of coupled systems with three independent angular momenta. the 9j symbol is related to sums over products of 6j symbols.
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