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  • #5423
    Kirill Danilov
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    The question doesn’t make sense because it convolutes multiple different properties. L and S are the quantum numbers for the electron orbital, the orientations are procured from the projections onto the z axis given by m_l and m_s which can take ranges of values between {-1, 0, 1}. The projections of J = 2 onto the z axis take the ranges between {-2, -1, 0, -1, -2} and correspond to different projections m_j = m_l + m_s, which may individually have different z axis projections. Looking at the total possibilities of m_j,

    m_l = -1, m_s = -1, m_l = -1, m_s = 0, m_l = -1, m_s = 1
    m_l = 0, m_s = -1, m_l = 0, m_s = 0, m_l = 0, m_s = 1
    m_l = 1, m_ s = -1, m_l = 1, m_s = 0, m_l = 1, m_s = 1

    m_j = -2, m_j = -1, m_j = 0
    m_j = -1, m_j = 0, m_j = 1
    m_j = 0, m_j = 1, m_j = 2
    of which m_j = -1, m_j = 0, and m_j=1 can also be achieved from J=1 and J=0.

    it is clear that J = 2 includes coupling of spins and orbits that are not aligned in their z axis projections and have different orientations. However for all cases if the spin and orbit are coaligned and m_j = 2 or -2, J must equal 2. Otherwise the value of J does not intrinsically speak to the orientation of L to S, only whether the coupling is expressed by their sum, difference or non-interaction.

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