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 / 1

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- Solution 1

Solution

The canonical Poisson bracket is

{f, g} = \sum_{k} (\frac{\partial f}{\partial q _{k}} \frac{\partial g}{\partial p _{k}} - \frac{\partial f}{\partial p _{k}} \frac{\partial g}{\partial q _{k}}) .

The coordinate derivatives are Kronecker deltas, so direct substitution gives

{q_{i}, q_{j}} = 0, {p_{i}, p_{j}} = 0, {q_{i}, p_{j}} = δ_{ij} .

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