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Clebsch-Gordan decomposition

The tensor product of spin-

j_{1}

and spin-

j_{2}

irreducible representations decomposes into one copy of each spin

j = ∣ j_{1} - j_{2} ∣, ∣ j_{1} - j_{2} ∣ + 1, \dots, j_{1} + j_{2} .

The change-of-basis entries between uncoupled and coupled states are Clebsch--Gordan coefficients.

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