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