= Unfolding a reflected interval trajectory
Reflecting an interval repeatedly across its endpoints maps a reflected path to a free path in an image interval. A return trajectory from $q\in(0,L)$ ends at $q+2rL$ after an even number of wall reflections, or $-q+2rL$ after an odd number. An <infinite square well> has reflection amplitude $-1$, so the corresponding <Dirichlet heat kernel on an interval> is the difference of direct and mirrored free kernels. Individual straight paths illustrate the geometry; the <path integral> sums all time-sliced paths with the same endpoints.
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