"It is left as a problem for the reader to show that if [itex][S,T][/itex] commutes with S and T, then [itex][e^{tT}, S] = -t[S,T]e^{tT}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

I'm not sure if i'm missing something here, but i dont even see how it is possible to arrive at this answer.

I get:

[tex][e^{tT}, S] = e^{tT}S - Se^{tT}[/tex]

Then using the fact that [itex][S,T][/itex] commutes with S and T this gives:

[itex]SST-STS = STS-TSS[/itex]

and

[itex]TST-TTS = STT-TST[/itex]

and see no way to go further.

One major thing is I don't even see how the factor of -t just appears in the identity?

[itex][e^{tT}, S] = -t[S,T]e^{tT}[/itex]

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# Problem understanding operator algebra

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