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Math Help - alternative expression of L^2

  1. #1
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    alternative expression of L^2

    show that L^2 may be alternative expressed as
    L^2 = L_{0}^{2} + L_0 + L_{-}L_{+} = L_{0}^{2} - L_0 + L_{+}L_{-}
    and that [L^2, L_{\alpha}] = 0 for \alpha = 1, 2, 3

    i know that the generators are L_{\alpha} = ix_{\alpha}
    and L_+ = L_1 + iL_2, L_- = L_1 - iL_2
    but i can't get L^2 = L_{0}^{2} = L_0 + L_{-}L_{+} = L_{0}^{2} - L_0 + L_{+}L_{-} no matter which way i try it!

    what is L^2 anyway? is it (x_1 x_2 x_3)^2?
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  2. #2
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    Re: alternative expression of L^2

    or is L^2 = L_1^2 + L_2^2 + L_3^2?
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