Ch 13.2 The three $2\times 2$ matrices $\sigma_x = \begin{pmatrix}0&1\\1&0\end{pmatrix}$, $\sigma_y = \begin{pmatrix}0&-i\\i&0\end{pmatrix}$, $\sigma_z = \begin{pmatrix}1&0\\0&-1\end{pmatrix}$. The spin operators for spin-1/2 are $\hat{S}_i = (\hbar/2)\sigma_i$. The Pauli matrices satisfy $\sigma_i\