Question: Given two matrices $A$ and $B$ satisfying the commutation relation $$begin{equation*} [A, B]=B tag{6.408} end{equation*}$$ calculate $$begin{equation*} exp (i alpha A) B exp (-i alpha

Given two matrices $A$ and $B$ satisfying the commutation relation

$$\begin{equation*}
[A, B]=B \tag{6.408}
\end{equation*}$$

calculate

$$\begin{equation*}
\exp (i \alpha A) B \exp (-i \alpha A) \tag{6.409}
\end{equation*}$$

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