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Benedict Irwin added Another Method.tex
almost 10 years ago
Commit id: 7258c34e6ddb46c75665c70de967d218040f32db
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\section{Another Method}
Another method to try is 3 (or 6 really) operators, for example \begin{equation}
a^r_{+}|\alpha>=\sqrt[3]{\alpha}|\alpha+\frac{2}{3}> \\
a^r_{-}|\alpha>=\sqrt[3]{\alpha}|\alpha-\frac{1}{3}> \\
a^g_{+}|\alpha>=\sqrt[3]{\alpha-\frac{1}{3}}|\alpha+\frac{2}{3}> \\
a^g_{-}|\alpha>=\sqrt[3]{\alpha-\frac{1}{3}}|\alpha-\frac{1}{3}> \\
a^b_{+}|\alpha>=\sqrt[3]{\alpha+\frac{1}{3}}|\alpha+\frac{2}{3}> \\
a^b_{-}|\alpha>=\sqrt[3]{\alpha+\frac{1}{3}}|\alpha-\frac{1}{3}> \\
\end{equation}
Then is was found that the combination \begin{equation}
a^r_+a^g_-a^b_+|\alpha>=(\alpha+\frac{1}{3})|\alpha+1>
\end{equation}
