Baker-Campbell-Hausdorff formula

See https://en.wikipedia.org/wiki/Baker%E2%80%93Campbell%E2%80%93Hausdorff_formula?wprov=sfti1#

$e^X{e}^Y=e^{X+Y+\frac{1}{2}[X,Y]+\frac{1}{12}[X,[X,Y]]-\frac{1}{12}[Y,[X,Y]]+\dots }$. If $X,Y$ commute we can ignore the higher order terms.

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Quantum Theory for Mathematicians is a good yet heavy source for the derivation of the above.