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I was wondering, is there a way to derive the expression for these coefficients without the use of the general CGC formula?

For example, the J=0 case (this is taken from wikipedia)

The 1/sqrt term is clear but the (-1)^.. term not so much, is there a way to find this coefficient?

I have read it requires the use of spinors and so on but I was wondering if there was a more simple way?

I found a derivation of the CGC using only binomial expansions, but it was difficult to see exactly how they saw the starting point, it seemed like it must have been educated guesses until worked. Other derivations of the coefficients rely on the J=0 coefficients or more advanced mathematics.

Thanks,

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# Fining Clebsch-Gordan coeffs in special cases, alternate method

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