- #1

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I tried by Taylor expanding the exponential, but I get [itex]-iEta[/itex] to first order, which seems wrong.

- Thread starter gentsagree
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- #1

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I tried by Taylor expanding the exponential, but I get [itex]-iEta[/itex] to first order, which seems wrong.

- #2

mfb

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Why does it seem wrong?

- #3

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[tex]e^{iHt}ae^{-iHt}=e^{-iEt}a[/tex]

which is said to be justified by [itex][H,a]=-Ea[/itex].

If I take my result to be true, I get

[tex]e^{iHt}ae^{-iHt}=e^{iHt}(e^{-iHt}a-iEta)=a-ie^{iHt}Eta[/tex]

- #4

mfb

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The first order is not the final result...

- #5

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Second order does the job....thanks.

- #6

mfb

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I am surprised by that, as the final result has all orders, and just ignoring orders means changing the value of things.Second order does the job....thanks.

- #7

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- #8

mfb

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Ah, okay.

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