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.
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