Answer by Ben Grossmann for If $[A,B]=B$. Calculate $e^{iA}Be^{-iA}$
I assume that these are matrices with $[A,B] = AB - BA$.Hint: Using the fact that $\frac d{dt} e^{tA} = Ae^{tA} = e^{tA}A$, verify that$$\frac d{dt} [e^{tA}Be^{-tA}] = e^{tA}[A,B]e^{-tA}$$
View ArticleIf $[A,B]=B$. Calculate $e^{iA}Be^{-iA}$
If $[A,B]=B$. Calculate\begin{equation*}e^{iA}Be^{-iA}\end{equation*}From this, We know that\begin{equation*}\begin{gathered}e^{iA}Be^{-iA} = (\mathbb{I} + iA...
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