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How do we show that the state [tex] |\chi>=\frac{1}{\sqrt{2}}(|\uparrow>|\downarrow>-|\downarrow>|\uparrow>)[/tex] has total spin zero? Does it involve acting some combination of the spin operators on it?
I know that the total spin operator [tex]\underline{S^2}=S_x^2+S_y^2+S_z^2=\frac{3\hbar^2}{4}I [/tex] where I is the 2x2 identity matrix but I don't see how that helps.
I know that the total spin operator [tex]\underline{S^2}=S_x^2+S_y^2+S_z^2=\frac{3\hbar^2}{4}I [/tex] where I is the 2x2 identity matrix but I don't see how that helps.