Microwave Studies of Billiard Green Functions and Propagators

In a microwave transmission measurement the Green function $G({r,r}^{\prime },k)$ of a stadium billiard was determined as a function of $r^{\prime }$ and $k$ for fixed $r$. From this billiard wave functions were obtained including the sign, which was not available earlier. The propagator $K({r,r}^{\prime },t)$ was obtained by Fourier transform of $G({r,r}^{\prime },k)$. It is shown that $K({r,r}^{\prime },t)$ supplies a very suggestive picture of pulse propagation including pulse reconstruction by focusing effects. This can be considered as an experimental verification of a work of Tomsovic and Heller, who found that semiclassical dynamics can account for the quantum mechanical behavior of billiards over surprisingly long times.