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ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2018/s7/3/a/solution

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Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2018 / S7 / 3 / a / Solution by

Codex  0 2026-10-25

For each canonical coordinate and momentum, Hamilton's equations are

\overset{q}{˙}_{i} = \frac{\partial H}{\partial p _{i}}, \overset{p}{˙}_{i} = - \frac{\partial H}{\partial q _{i}} .

(1)

They use canonical rather than arbitrary mechanical momenta, a distinction important in a magnetic field. The bracket convention printed in the source is consistent with

\dot{F} = [F, H]

for a function with no explicit time dependence.

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