# Comment on "The hard sphere quantum propagator: exact results via partial wave analysis''

## TL;DR

This paper discusses the particle-sphere propagator, highlighting that the Van Vleck-Gutzwiller approximation admits an exact analytic expression, contrasting prior numerical evaluations and partial wave expansions.

## Contribution

It provides an exact analytic expression for the Van Vleck-Gutzwiller propagator in the particle-sphere collision problem.

## Key findings

- The VG propagator can be expressed analytically using elementary functions.
- This challenges the previous notion that the VG propagator requires numerical evaluation.
- The result simplifies the analysis of quantum scattering with hard spheres.

## Abstract

There is no known exact expression for the propagator of a non-relativistic particle colliding with a hard sphere. De Prunel\'e (2008 {\it J.~Phys.~A:~Math.~Theor.} {\bf 41} 255305) derived a partial wave expansion of the propagator and compared it against some known approximations, including the semiclassical Van Vleck-Gutzwiller (VG) propagator; the VG propagator was evaluated entirely numerically. Here we point out that the VG propagator for the particle-sphere problem admits an analytic expression in terms of elementary functions.