 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/32d/a/solution

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

The transformations obey

g_{1}^{s} g_{1}^{r} = g_{1}^{s + r}

and

g_{1}^{0}

is the identity. If

x (t) = x (t) + s t

, then

d^{2} x / d t^{2} = d^{2} x / d t^{2}

. Thus solutions of the free-particle equation are mapped to solutions, so this is a one-parameter group of Lie symmetries.

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