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Hello, I am going through this and I am totally confused. Where do they come up with ##\mid 1 \hspace {0.02 in} 0 \rangle = \frac {1}{\sqrt{2}}(\uparrow \downarrow + \downarrow \uparrow)##? They just use the lowering operator, but I'm wondering if the switch in order from equation 4.177 and the one right above it (not numbered) is significant?

Also, why is this thing called a "triplet" (I see three rows in equation 4.177, is that why?)

I guess my problem is to go from ## \mid s \hspace{0.02 in} m \rangle## to some sort of up down representation. How do I get the singlet, ##\mid 0 \hspace{0.02 in} 0 \rangle##?

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# Triplets/Singlets and applying lowering S operator

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