  We present a systematic approach to the linearised Yang-Mills-Higgs equations
in the background of a 't Hooft-Polyakov monopole and use it to unify and
extend previous studies of their spectral properties. We show that a
quaternionic formulation allows for a compact and efficient treatment of the
linearised equations in the BPS limit of vanishing Higgs self-coupling, and use
it to study both scattering and bound states. We focus on the sector of
vanishing generalised angular momentum and analyse it numerically, putting
zero-energy bound states, Coulomb bound states and infinitely many Feshbach
resonances into a coherent picture. We also consider the linearised
Yang-Mills-Higgs equations with non-vanishing Higgs self-coupling and confirm
the occurrence of Feshbach resonances in this situation.
