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Angular momentum operator

Addition of angular momentum

With $J=j_1+j_2$, the maximal state is the product $|J,J\rangle=|j_1,j_1\rangle|j_2,j_2\rangle$. Lowering it once gives
$$
|J,J-1\rangle=
\sqrt{\frac{j_1}{J}}|j_1,j_1-1\rangle|j_2,j_2\rangle
+\sqrt{\frac{j_2}{J}}|j_1,j_1\rangle|j_2,j_2-1\rangle.
$$
The orthogonal combination is the highest-weight state $|J-1,J-1\rangle$.


Highest-weight states in angular momentum addition

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 33B / a / iii / Solution

Highest-weight states in angular momentum addition

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Highest-weight states in angular momentum addition

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