Task 1

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    Bruno S.
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    When L and S are parallel and pointing in opposite directions, the energy of the state described by this spin-orbit coupling will have the lowest possible energy. Therefore this state is the bottom one, denoted by J=0.

    When L and S are parallel and pointing in the same direction, the energy of the state described by this spin-orbit coupling will have the maximal possible energy. This state is therefore the top one, denoted by J=2.

    The only remaining state is the one where L and S are perpendicular to each other, which will have an energy between the J=0 and J=2 state. It is therefore found in the middle of the left hand side diagram and denoted by J=1.

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