angular momentum algebra

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    mmvdwiel
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    We have |\overrightarrow{L}+\overrightarrow{S}|>|\overrightarrow{J}|>|\overrightarrow{L}-\overrightarrow{S}|. These vector sums imply that for parallel L and S that are pointed in the same direction, we can sum both values to obtain the value for |\overrightarrow{J}|, which is, as L=1 and S=1, 2. If the vectors L and S are in the opposite direction, these values have to be subtracted, so we obtain J=0. If the vectors L and S are perpendicular to each other, the value of the vector J will be the value of the vector which points to the same direction, parallel to the vector J. As L and S have the same value here, J will thus be 1.

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