Trying to get my head around this one. Given that you can have a proton and an electron in a hydrogen atom for example, and they can create a singlet or triplet configuration, with spin 1 and spin 0 respectively. The total spin operator can be derived as: S^2 = (Se + Sp)^2 = Se^2 + Sp^2 + 2Se.Sp Where the dot is the dot product, but then what you get is a bunch of Sx,Sz,Sy acting on the tensor products to provide eigenvalues and the eigenvectors out. The math is all well and good, but the problem I have is that the spin operators Sz,Sy and Sx don't commute, so how come you can just apply the operators to the respective spins to get out an answer, seems odd to me. Any help would be appreciated. Cheers.