Modification to the pre-factor of the semiclassical propagator

We modify the pre-factor of the semiclassical propagator to improve its efficiency in practical implementations. The new pre-factor represents the smooth portion of an orbit's contribution, and leads to fast convergence in numerical calculations. As an illustration of the accuracy and efficiency of the resultant propagator, we numerically calculate overlaps between quantum and semiclassical wave functions, as well as low-lying spectrum density in a 10-dimensional system containing unstable classical orbits. This sheds light on applying the semiclassical propagator to high-dimensional systems.