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\sect{Average distance between two particles in a box}

In a one dimensional box, with length ${L}$, two particles are
turning around. The particles don't know about each other. The
probability function for finding a particle in a specific place in
the box is uniform.

Let ${r}$ be the relative location of the particles.

Find ${f\left(r\right)dr={p}\left(r<\hat{r}<r+dr\right)}$
and also ${\langle\hat{r}\rangle}$ and ${\sigma_{r}}$, in two ways.