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I would be most grateful if someone would explain how do we calculate the spin function

χ(s_1,s_2 )=1/√2 [α(s_1 )β(s_2 )±α(s_2 )β(s_1 )]

both the symmetric and antisymmetric

α(s_1 )β(s_2 )+α(s_2 )β(s_1 ) = ?

α(s_1 )β(s_2 )-α(s_2 )β(s_1 ) = ?

knowing that α( + 1 / 2) = β( − 1 / 2) = 1 and α( − 1 / 2) = β( + 1 / 2) = 0.

And how do we get singlet (S=0, S_z=0) and triplet (S=1, S_z=+1,0,-1) states from this?

I have not found this explained explicitly anywhere, everybody seems to take it for granted, and it is really bothering me.

Thank you very much for possible clarification!

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# Homework Help: Singlet and triplet states

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