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Physics LibreTexts

7.4: Poisson’s Theorem

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If f and g are two constants of the motion (i.e., they both have zero Poisson brackets with the Hamiltonian), then the Poisson bracket [f,g] is also a constant of the motion. Of course, it could be trivial, like [p,q]=1 or it could be a function of the original variables. But sometimes it’s a new constant of motion. If f,g are time-independent, the proof follows immediately from Jacobi’s identity. A proof for time dependent functions is given in Landau—it’s not difficult.


This page titled 7.4: Poisson’s Theorem is shared under a not declared license and was authored, remixed, and/or curated by Michael Fowler.

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