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The time-derivative of an operator [itex] A(t) = U^\dagger a(t)U [/itex] in the heizenberg picture is given by:

[itex]\frac{dA(t)}{dt} = \frac{i}{\hbar} [H,A(t)] + U^\dagger(\frac{da(t)}{dt})U [/itex]

Now, I know that under some conditions, we can write:

[itex]\frac{dA(t)}{dt} = \frac{i}{\hbar} U^\dagger[H,a(t)]U + U^\dagger(\frac{da(t)}{dt})U [/itex]

My question is- what are those conditions?

thanks

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# Dynamics in the heizenberg picture

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