Relation between angular momentum quantum numbers We have the angular momentum quantum numbers $(j,l,s)$ representing total angular momentum, orbital angular momentum and spin respectively. 
I am solving a problem where we try to show that if you have two spin-1 particles then $l+s$ is even. I didn't understand how to relate these numbers together to be able to show this, so I tried to look at some Wikipedia pages, such as this one. I saw a relation which I thought may help solve the problem: $j=|l\pm s|$. However, I don't understand this equation - which value do you take, $+$ or $-$? 
Question:
Does this help solve my problem? If so can someone explain the $\pm$ part? If not, could someone guide me towards something that will help me solve the problem? An equation or relation perhaps, or a hint?
Thanks.
 A: When coupling two systems, one with angular momentum $\ell_1$ the other with angular momentum $\ell_2$, the possible values of the net angular momentum $J$ are those in the set $\{\ell_1+\ell_2,\ell_1+\ell_2-1,\ell_1+\ell_2-2,\ldots, \vert \ell_1-\ell_2\vert\}$, i.e. they range from the sum to the absolute value of the difference of $\ell_1$ and $\ell_2$.
In the simplest example of application of this rule, $\ell_1=\ell_2=1/2$ so the possible values of such a two-spin system would be $J=0$ and $J=1$.  
In general all possible values in the range will appear, although there might be some symmetry requirements that will eliminate some of the final $J$ values.  In the specific case of $\ell_1=\ell_2=1$, one can show using Clebsch-Gordan methods that the $J=2$ and $J=0$ states are symmetric under permutations of the particle labels, whereas $J=1$ is antisymmetric.  If the particles are indistinguishable bosons, this automatically eliminates the antisymmetric part $J=1$ in the list of possible $J$.  
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