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We now ask what are the allowed total spin states generated by adding the spins ${\bf S}= {\bf S}_1 + {\bf S}_2$ ,in fact, they are Singlet and Triplet Spin States

\left( \begin{array}{ll} |1,1\rangle & =\uparrow\uparrow\\ |1,0\rangle & =\frac{1}{\sqrt{2}}(\uparrow\downarrow + \downarrow\uparrow)\\ |1,-1\rangle & =\downarrow\downarrow \end{array} \right)\ s=1\ (\mathrm{triplet})

\left(|0,0\rangle=\frac{1}{\sqrt{2}}(\uparrow\downarrow - \downarrow\uparrow)\right)\ s=0\ (\mathrm{singlet})

so, when s=1 and m=0, many people call it state of parallel spin, but i dont think so , and i also dont understand the state . (or s=1,m=0 ) can you help me? thanks!