Consider a spin-1 particle that is a bound state of two particles of spin-1/2. How do you write the state $\left|\alpha\right\rangle$ if
- the two particles are distinguishable?
- the two particles are identical?
Since the two particles can combine in $S=0,1$ states, orbital angular momentum can take the values $$S=0 \; \longrightarrow \; \ell=1,$$ $$S=1 \; \longrightarrow \; \ell=0,1,2.$$ If the two particles are identical, the state ket must be antisymmetric, so it's only possible to have $$S=1, \;\;\; \ell=1.$$ But I can't understand how to write $\left|\alpha\right\rangle$.