Benedict Irwin edited Old QFT.tex  almost 10 years ago

Commit id: cfdbc97f0b15e5a613dd0bdc1cb02c3574e07815

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we know that \begin{equation}  [a,a^+]=1=[a,a^+1,1] [a,a^+]=1=[a,a^+,1]  \end{equation}  So trying \begin{equation}  [a,a^+,a]|n>=2n\sqrt{n}|n-1>-(n+1)\sqrt{n}|n-1>-(n-1)\sqrt{n}|n-1>=0  \end{equation}  Meaning \begin{equation}  2aa^+a=aaa^+ + a^+aa  \end{equation}