 Solution

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/2017/s7/3/b/solution

To match the source's order define

[a, b] = \sum_{i} (a_{p_{i}} b_{q_{i}} - a_{q_{i}} b_{p_{i}})

\frac{d g}{d t} = g_{t} + [H, g] .

[H, H] = 0

, hence

d H / d t = H_{t}

, which vanishes for a time-independent Hamiltonian. With the alternative common convention

{a, b} = \sum_{i} (a_{q_{i}} b_{p_{i}} - a_{p_{i}} b_{q_{i}})

, the same law is

d g / d t = g_{t} + {g, H}

; mixing the two orders would reverse the physical time evolution.

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