## Heisenberg's equation of motion

The equation of motion for an observeable A is given by $\dot{A} = \frac{1}{i \hbar} [A,H]$.

If we change representation, via some unitary transformation $\widetilde{A} \mapsto U^\dag A U$ is the corresponding equation of motion now

$\dot{\widetilde{A}} = \frac{1}{i \hbar} [\widetilde{A},U^\dag H U]$
or
$\dot{\widetilde{A}} = \frac{1}{i \hbar} [\widetilde{A},H]$?

I'm asking because I want to write the time derivative of the Dirac representation of the position operator in the Foldy-Wouthusyen representation.

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 Blog Entries: 9 Recognitions: Homework Help Science Advisor If you know how to derive Heisenberg eq of Motion, then you should have no problem to find the answer.
 Recognitions: Homework Help They're the same, the first equation of motion for the operator UAUt gives the second EOM for A.

## Heisenberg's equation of motion

Are you saying that the transformed operator satisfies the first equation but not the second?

 Recognitions: Science Advisor If the generator of the unitary transform U depends on t -- like going from Schrodinger picture to the Interaction Picture -- then noospace, you have left out a term. Standard stuff, can be found in most QM or QFT texts. Regards, Reilly Atkinson

Recognitions:
Homework Help
 Quote by noospace I'm asking because I want to write the time derivative of the Dirac representation of the position operator in the Foldy-Wouthusyen representation.
see Messiah QM vol 2.