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Heisenberg picture

In the Heisenberg picture, states are fixed and an observable evolves as

A_{H} (t) = U (t)^{†} A_{S} U (t) .

For a time-independent Schrödinger-picture observable,

\frac{d A _{H}}{d t} = \frac{i}{ℏ} [H, A_{H}] .

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