  We consider the scattering of particles by an obstacle which tunnels
coherently between two positions. We show that the obstacle mimics two
classical scatterers at fixed positions when the kinetic energy epsilon of the
incident particles is smaller than the tunnel splitting Delta: If the obstacles
are arranged in parallel, one observes an interference pattern as in the
conventional double-slit experiment. If they are arranged in series, the
observations conform with a Fabry-Perot interferometer. At larger epsilon
inelastic processes result in more complex interference phenomena. Interference
disappears when epsilon >> Delta, but can be recovered if only the elastic
scattering channel is detected. We discuss the realization of a quantum
obstacle in mesoscopic systems.
