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## Main Question or Discussion Point

I was just going through the calculation to go from the top line to the bottom and was just not arriving at the same result. Working backwards and just looking at the first term (i.e. the one with coefficient ##g_L## I get):

## \frac {J^2 + J + L^2 + L - S^2 - S}{2(J^2 + J)} = \frac {L^2 + S^2 + 2LS + L + S + L^2 + L - S^2 - S}{2(L^2 + S^2 + 2LS + L + S)} = \frac{L^2 + LS + L}{J(J + 1)} ## (assuming L and S commute)

Although this is not equivalent to the above expression and it appears I am missing something very basic. Any help with this would be great.