Singlet state
= Singlet state
{wiki}
= Angular momentum singlet state
{synonym}
= Rotation singlet
{synonym}
Two equal spins $j$ have the unique total-spin-zero state
$$
|0,0\rangle=\frac1{\sqrt{2j+1}}
\sum_{m=-j}^j(-1)^{j-m}|j,m\rangle|j,-m\rangle.
$$
It is invariant under joint rotations.
A <singlet state> is the one-dimensional rotation representation; this construction supplies the angular-momentum-zero case for two equal spins.