[en] An exact expression for the partial wave hard sphere quantum propagator in three-dimensional space is given in terms of the Fourier transform of an expression involving spherical Bessel functions. For the s wave case, the Fourier transform is calculated analytically. This Fourier transform is also evaluated for the general case by contour integration in terms of a Laplace transform and residues contributions. The accuracy of previous approximations for a hard sphere quantum propagator can thus be evaluated. In particular, the Van Vleck-Gutzwiller classical approximation is found to be very accurate provided that the classical action is greater than only a few units of reduced Planck constant