Could somebody please explain what is going on here?
We have a system of two indistinguishable spin-1 bosons. We shall adopt the center of mass frame.
$S$ = total spin
$L$ = relative orbital angular momentum
$J$ = $L+S$ = total angular momentum
Prove that $J = 2m$ where $m$ is an integer. If given that $J=1$, what are the permissible $(L,S)$ pairs?
I am lost with this. I have managed to show that for the states $S=0, S=2$ interchanging particles $1,2$ is symmetric, whereas it is antisymmetric for $S=1$. However, I don't know how to use this here. What is the significance of the CoM frame choice?