1. The problem statement, all variables and given/known data So i have to calculate the Clebsch-gordan coefficients for the state j1=3/2 and j2=1/2 2. Relevant equations Recursiom formula, lowering and uppering operator 3. The attempt at a solution I have tried to calculate the first set of the coefficients stating that: L- l2,2> = L- l3/2,1/2>l1/2,1/2> For the left side I got that it is equal to 2hl2,1>. Is that correct? I can't get the right coefficients on the right side. In general, I have trouble understanding which combinations of j and m to use tobget what I have to do. Is there some procedure to get all of them in order? Right now I am trying to guess what to use and see if I get the right combination.