Recent content by Marvelant

I'm not confident enough in tensor products to work at that level, unfortunately.

Would it be a linear combination of ## \rvert 1/2,-1/2 \rangle_1 \rvert 1,1 \rangle_1 ## and ## \rvert 1/2,1/2 \rangle_1 \rvert 1,0 \rangle_1 ##?

I suppose I could do the same for ## \rvert 1/2,1/2 \rangle ##.

Can I generate these by applying the lowering operator to the highest ket like this? $$ S_- \rvert 3/2,3/2 \rangle = (S_{1-}+S_{2-}) \rvert 1/2,1/2 \rangle_1 \rvert 1,1 \rangle_2 $$

Sorry for the confusing notation, all I meant was that I added together every possible pair, one element from each set, and discarded any repeated values. I suppose discarding the repeated values was the wrong move, since the degeneracy would depend on them. So I'm going to guess degeneracies...

I suppose all the different combinations would be ## \{ -1/2, 1/2 \} + \{ -1, 0, 1 \} = \{ -3/2, -1/2, 1/2, 3/2 \} ## which translates to ## s = \{ 1/2, 3/2 \}## with ## \vec{S}^2## eigenvalues of ## (3/4) \hbar^2, (15/4) \hbar^2##

Homework Statement Given 3 spins, #1 and #3 are spin-1/2 and #2 is spin-1. The particles have spin operators ## \vec{S}_i, i=1,2,3 ##. The particles are fixed in space. Let ## \vec{S} = \vec{S}_1 + \vec{S}_2 + \vec{S}_3 ## be the total spin operator for the particles. (ii) Find the eigenvalues...