classical motion. However, we note that as we go from the COE to the Poisson limits, the fits to the $\chi^2$ get worse. Note especially the shift of the maxima away from zero. This discrepancy is connected to the fact that the results are strongly basis dependent when not in the universal COE limit.

Semiclassical correspondences
-----------------------------

We can now make a direct comparison between the classical and quantum results by employing a phase space approach. To do this, we use the Husimi representation of the QEF. The Husimi distribution, interpreted as a probability density, is a coarse-grained version of the Wigner function which goes smoothly to the semiclassical limit[@chang]. In practice, the most often used technique of coarse-graining is to take the overlap of the QEF with coherent oscillator states. For the radial coordinate the coherent state is $$\Psi_{r_0,p_0}^G(r) = ({\sigma\over\pi{\tilde\hbar}})^{1\over 4}\,
\exp\left\{-{\sigma\over 2{\tilde\hbar}}(r - r_0)^2 + i{p_0\over 
{\tilde\hbar}}(r - {r_0\over 2}) \right\},$$ which is a minimum-uncertainty Gaussian wavepacket centered at $(r_0,p_0)$, with root mean-squared deviations given by $\Delta\rho = \sqrt{{\tilde\hbar}/2\sigma}$, $\Delta p = 
\sqrt{{\tilde\hbar}\sigma/2}$, and $\sigma\,$ is the ‘squeezing’ parameter. This parameter is adjusted when making comparisons to the classical phase-space plots. The Husimi distribution of a single 