Spin-dot-product eigenvalue
= Spin-dot-product eigenvalue
For two spins of magnitude $s$, $\mathbf S_1\mathbin\cdot\mathbf S_2=\tfrac12(\mathbf J^2-\mathbf S_1^2-\mathbf S_2^2)$. For two spin-one particles its eigenvalues in total-spin sectors $J=0,1,2$ are $-2,-1,1$ in units of $\hbar^2$.