The particular form of the \(2 \times 2\) matrices corresponding to the operators \(\hat{\boldsymbol{\sigma}}\) and \(\hat{I}\) in Eq. (98a) depends on the basis selected for the spin state representa...The particular form of the \(2 \times 2\) matrices corresponding to the operators \(\hat{\boldsymbol{\sigma}}\) and \(\hat{I}\) in Eq. (98a) depends on the basis selected for the spin state representation; for example, in the standard \(z\)-basis, in which the Cartesian components of \(\hat{\boldsymbol{\sigma}}\) are represented by the Pauli matrices (4.105), the \(4 \times 4\) matrix form of Eq. (98a) is \[\alpha_{x}=\left(\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ …
