Adding Angular Momenta: Rules of Thumb?

[Heirot]

Hello,

I was wondering is there a way (a rule of the thumb, perhaps) to tell which states after addition of angular momenta are (anti)symmetric?

For example:

1/2 x 1/2 = 1 + 0, 1 is a symmetric triplet state, while 0 is an antisymmetric singlet state.

How does this generalize to, e.g.

1/2 x 1/2 x 1/2 = 3/2 + 1/2 + 1/2, or
1 x 1 = 2 + 1 + 0?

Thank you!

 

[Avodyne]

For the product of two identical ang.mom., the largest is symmetric, then they alternate between sym and anti-sym as you go down.

For three or more, you have more complex symmetry classes to deal with (eg Young tableaux are useful). But the highest resulting ang.mom. is always fully symmetric (the Young tableaux is a single row).

 

[LAHLH]

I would recommend the discussion in Jones-Groups representations and physics (I think it's ch8) for a very easy going introduction to this stuff.