Spin-one-half triplet state
= Spin-one-half triplet state
= Triplet state
{synonym}
The symmetric two-particle states
$$
|\uparrow\uparrow\rangle,
\qquad
\frac{|\uparrow\downarrow\rangle+|\downarrow\uparrow\rangle}{\sqrt2},
\qquad
|\downarrow\downarrow\rangle
$$
form the spin-one triplet. On this subspace, $\mathbf S^2$ has eigenvalue $1(1+1)\hbar^2=2\hbar^2$.