  A spectral wall is a surface in a moduli space of classically BPS solitons
where an internal excitation crosses the continuum mass threshold. It has
recently been shown that spectral walls in classical field theory repel
solitons whose corresponding internal excitations are excited. We investigate,
for the first time, the fate of spectral walls in a quantum theory, calculating
the instantaneous acceleration of a wave packet of classically BPS antikinks in
the presence of an impurity. We find that, in the quantum theory, the antikinks
are repelled even when the bound mode is not excited. Perhaps due to this
repulsive force, the dramatic classical effects of the spectral wall are not
seen in our quantum calculation.
