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

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

[itex]\dot{\widetilde{A}} = \frac{1}{i \hbar} [\widetilde{A},U^\dag H U][/itex]

or

[itex]\dot{\widetilde{A}} = \frac{1}{i \hbar} [\widetilde{A},H][/itex]?

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

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

[itex]\dot{\widetilde{A}} = \frac{1}{i \hbar} [\widetilde{A},U^\dag H U][/itex]

or

[itex]\dot{\widetilde{A}} = \frac{1}{i \hbar} [\widetilde{A},H][/itex]?

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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