 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/8b/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For

Q = p

and

P = λ q

{Q, P}_{q, p} = - λ .

The map is therefore canonical only for

λ = - 1 .

Then

Q = p

and

P = - q

Φ (q, Q) = qQ

gives

p = Φ_{q} = Q, P = - Φ_{Q} = - q,

as required.

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