Wave tails in non-trivial backgrounds

It is well known that waves propagating in a non-trivial medium develop 'tails'. However, the exact form of the late-time tail has so far been determined only for a narrow class of models. We present a systematic analysis of the tail phenomenon for waves propagating under the influence of a general, spherically symmetric scattering potential. It is shown that, generically, the late-time tail is determined by spatial derivatives of the potential. The analytical results are confirmed by numerical calculations.