L and S coupling

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    Kaat Spoormans

    The ‘parallel and pointing in opposite directions’ orientation corresponds to the J=0 case. The spins with the same length cancel each other when they are antiparallel.

    The ‘perpendicular to each other’ orientation corresponds to the J=1 case. When you add two perpendicular vectors, in one direction the vectors will cancel each other, but in the other direction, the vectors will add up. But they cannot add to 2 times their initial length, because part of it cancelled, so the only case left is J=1.

    The ‘parallel and pointing in the same direction’ orientation corresponds to the J=2 case. Now the vector all totally aligned, so their is no part which will cancel and tho total lengths are added which result in the J=2 case.

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