At time \(t=0\), a collection of classical particles is in equilibrium at temperature \(T\) in a threedimensional harmonic oscillator potential \(V(\boldsymbol{r})=\frac{1}{2} m \omega_{0}^{2}|\boldsymbol{r}|^{2}\). At \(t=0\), the harmonic potential is abruptly removed. Use the momentum distribution at \(t=0\) to determine the spatial density at time \(t>0\). Show that this is equivalent to the high temperature limit of equation (7.2.15).