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    The question is to find the isospin coupling of a pion(+), pion(-) and a pion(0) by deriving the isospin function.

    I obtain the answer:
    sqrt(1/10)|3 0> + ((3-sqrt(3))/6)|2 0> +((sqrt(30)-5sqrt(2))/10)*|1 0>+ sqrt(6)/6 *|0 0>
    But this doesn't seem right as the coefficients squared do not add up to 1. Did I take the right approach or am I doing it wrong?


    My method:

    So this is what I did: I found |1 -1>|1 0>=sqrt(1/2)(|2 -1> -|1 -1> ) by reading off the CG table.
    Then to find |1 1>|1 -1>|1 0>, I did |1 1>|1 -1>|1 0>=sqrt(1/2)(|2 -1>|1 1> -|1 -1>|1 1> )by multiplying the line before by |1 1>
    So I found |2 -1>|1 1>=sqrt(1/5)|3 0>-sqrt(1/2)|2 0>+sqrt(3/10)*|1 0>
    And also |1 -1>|1 1>=sqrt(1/6)|2 0>-sqrt(1/2)|1 0>+sqrt(1/3)*|0 0>
    Hence, after simplifying down I end up with the answer above
 
 
 
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