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I was told that this is true but that you cannot construct J=1/2 states directly, moreover that the coefficients are relative?

Homework Statement So I'm told I can't do it this way but I was wondering if anyone could clarify as to why? We're given |J=\frac{1}{2},M = \frac{1}{2}\!> where j_1 = 1 \, and \, j_2 = \frac{1}{2} Homework Equations The Attempt at a Solution So this can be composed as a linear...