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Benedict Irwin edited Matrix Generators.tex
over 9 years ago
Commit id: b3616ec487d1d9fa8972ab2c920e0569ef181dc5
deletions | additions
diff --git a/Matrix Generators.tex b/Matrix Generators.tex
index 37cb2dc..4f7198a 100644
--- a/Matrix Generators.tex
+++ b/Matrix Generators.tex
...
\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}