  We present a semiclassical approximation to the scattering wavefunction
$\Psi(\mathbf{r},k)$ for an open quantum billiard which is based on the
reconstruction of the Feynman path integral. We demonstrate its remarkable
numerical accuracy for the open rectangular billiard and show that the
convergence of the semiclassical wavefunction to the full quantum state is
controlled by the path length or equivalently the dwell time. Possible
applications include leaky billiards and systems with decoherence present.
