I was wondering if someone could help me to understand how you combine spin to form the total spin angular momentum number, S. Here's a selection from my notes:(adsbygoogle = window.adsbygoogle || []).push({});

Now as I understand it, [tex]S = (s_1 + s_2), (s_1 + s_2 - 1), ... |s_1 - s_2|[/tex]. However, I don't really see how that leads to the conclusion that the singlet state above has S=0 and the triplet state has S=3.

And even if I can find a way to rationalise it for the 2 quark case, I don't have a clue what's going on when you add the third quark to S=0. I mean, I get that the spin of a quark is 1/2 so adding it to S=0 gives you S=3/2, but I don't see how S=1/2 corresponds to the states:

[tex]\frac{1}{\sqrt{2}} \left(\uparrow \downarrow \uparrow - \downarrow \uparrow \uparrow \right)[/tex] and [tex]\frac{1}{\sqrt{2}} \left(\uparrow \downarrow \downarrow - \downarrow \uparrow \downarrow \right)[/tex]

Could someone kindly explain this to me?

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# Working out total spin ?

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