- #1

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Let's say I have two spin 1/2 particles, so

[tex]J=S_1+S_2[/tex]

and |J| ranges from [tex]|S_1 + S_2|[/tex] to [tex]|S_1 - S_2|[/tex]

in this case J=1 is triplet and J=0 is singlet.

Now how do you find the J=0 state? I know that

[tex]|j=0,m_j=0>=\frac{1}{\sqrt{2}}(\uparrow_1 \downarrow_2 - \downarrow_1 \uparrow_2)[/tex]

but how do you get this in the first place? Is it pretty much trial and error and then use operator to generate rest of the states for that particular J? Or is there an algorithm for finding state [tex]|j,m_j=j>[/tex]?