I have a pair of non interacting, identical 1/2 spin fermions in a one dimensional infinite square well with walls at x=0 and x=L. One particle is in ground state, the other in first excited state. This two-particle system has total spin quantum number S=0 I have normalized energy eigenfunctions for each and am trying to explain implication of this to symmetries of spin and spatial parts of the total wave function which I think is; ψ1.2(t) = ψ(x1, x2, t) Ims1, ms2> or for time t=0 ψ1.2 = ψ(x1, x2) Ims1, ms2> So what exactly is the total spin quantum number please. I can see that the spin quantum number of a spin 1/2-particle is 1/2. So could the total spin quantum number be when adding the second part of the pair? Additionally, if this total spin quantum number becomes S=1 when they are both in the same eigenstate what does this relate to? Are both particles now either spin-up or both spin-down?