Benedict Irwin edited Matrix Generators.tex  over 9 years ago

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\end{bmatrix}  \end{equation}  Ladder operators \begin{equation}  \begin{vmatrix}  \textbf{i} & 0 \\ 0 & \textbf{j}  \end{vmatrix}  =  \begin{bmatrix}  0 & 1 \\ 0 & 0  \end{bmatrix}  =a \\  \begin{vmatrix}  \textbf{j} & 0 \\ 0 & \textbf{i}  \end{vmatrix}  =  \begin{bmatrix}  0 & 0 \\ 1 & 0  \end{bmatrix}  =a^\dagger\\  \begin{vmatrix}  \textbf{i} & 0 \\ 0 & \textbf{i}  \end{vmatrix}  =  \begin{bmatrix}  1 & 0 \\ 0 & 0  \end{bmatrix}  =aa^\dagger\\  \begin{vmatrix}  \textbf{j} & 0 \\ 0 & \textbf{j}  \end{vmatrix}  =  \begin{bmatrix}  0 & 0 \\ 0 & 1  \end{bmatrix}  =a^\daggera  \end{equation}