Given a system of two identical particles (let's say electrons), of (max) spin 1/2 (which means the magnetic quantum number of each of the electrons can be either 1/2 or -1/2), how can we write the operators (total angular momentum, z-component of the total angular momentum etc.) (a) in the uncoupled basis and (b) in the uncoupled basis? Please be specific and give numerical examples. First, my problem is that I don't know how to write an operator in either the coupled or the uncoupled basis, and I really searched the internet and a few well-known quantum mechanics books (e.g. Griffiths). Please help.