  We calculate the energy spectrum of quasiparticles trapped by a domain wall
separating different time reversal symmetry-breaking ground states in a
hexagonal superconductor, such as UPt$_3$. The bound state energy is found to
be strongly dependent on the gap symmetry, the domain wall orientation, the
quasiparticle's direction of semiclassical propagation, and the phase
difference between the domains. We calculate the corresponding density of
states and show how one can use its prominent features, in particular, the
zero-energy singularity, to distinguish between different pairing symmetries.
