I have been following a series of Leonard Susskind's lectures called 'Quantum Entanglements' (Part 1). In general, he explains how to find the probabilities of measurements of spin ½ particles' states, both single particles and pairs of them. I have learned the following: how to use the 2x2 spin matrices for single particles, and the 4x4 spin matrices for pairs of particles, how to construct projection operators to help with the calculations and how to find the probabilities of the results of measurements of different states, using the projection operators (I may have missed a few things). Now that I understood, to an extent that I was happy with, how to work with these spin ½ particles, I wanted to move on to looking at spin 1 particles. I have found the 3x3 spin matrices and their eigenvectors, but then I have no clue whether I can construct the projection operators in the same way that I did from the spin ½ matrices. Is this possible or is it more difficult than that? (I can't see how it is possible myself, as the original equation for the projection operators was ½(I ± Sn), where the '±' is a '+' for a measurement of the spin being up and '-' for a measurement of the spin being down, but since there are three possible outcomes for the measurement of the spin of a spin 1 particle, this doesn't seem to work) It is difficult for me to stick to the post template as this is more of an adventure into a new area of physics rather than a set assignment, but if it helps, the work I have done so far, for spin half particles, is here (effectively the relevant equations): LINK Thanks for any help in advance.