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Benedict Irwin added Fermionic Half Operators.tex
almost 10 years ago
Commit id: f6a6cd148b2d203fef43033b378362a2a98f2f7e
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\section{Fermionic Half Operators}
Seek to create the fermionic creation and annihilation operators \begin{equation}
b|n>=\sqrt{n}|n-1> \\
b^+|n>=\sqrt{1-n}|n+1>
\end{equation}
which only accept occupancies of 0 and 1. It can be seen that the definition of the annihilation operator is the same, and it will still be such that $b=sr$, however for $b^+=r^+s^+$ we must define the fermionic half operators \begin{equation}
s^+|n>=\sqrt[4]{1-n}|n+\frac{1}{2}> \\
r^+|n>=\sqrt[4]{\frac{3}{2}-n}|n+\frac{1}{2}
\end{equation}
