%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}