Spin one-half
= Spin one-half
{title2=$\mathbf S=\boldsymbol\sigma/2$}
In units $\hbar=1$, spin one-half is the two-dimensional irreducible <spin angular momentum> representation with components $S_i=\sigma_i/2$. The <Pauli matrices> give <eigenvalues> $\pm1/2$ along every unit axis. The normalized $x$-axis states are $(|\uparrow_z\rangle\pm|\downarrow_z\rangle)/\sqrt2$.