Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S7 / 3 / 2 / Solution

For a phase-space function with no explicit time dependence, the chain rule and Hamilton's equations give

\frac{df}{d t} = \sum_{i} (\partial_{q_{i}} f \overset{q}{˙}_{i} + \partial_{p_{i}} f \overset{p}{˙}_{i}) = \sum_{i} (\partial_{q_{i}} f \partial_{p_{i}} H - \partial_{p_{i}} f \partial_{q_{i}} H) = {f, H} .

An explicitly time-dependent function would instead satisfy

df / d t = \partial_{t} f + {f, H}

.

 Ancestors (12)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version