  We consider the problem of bound states in strongly anisotropic ferromagnetic
impurities in a superconductor, motivated by recent experiments that claim to
observe Majorana modes at the ends of ferromagnetic wires on a superconducting
substrate [S. Nadj-Perge et al., Science 346, 602 (2014)]. Generalizing the
successful theory of bound states of spherically symmetric impurities, we
consider a wire-like potential using both analytical and numerical approaches.
We find that away from the ends of the wire the bound states form bands with
pronounced van Hove singularities, giving rise to subgap peaks in the local
density of states. For sufficiently strong magnetization of the wire, we show
that this process generically produces a sharp peak at zero energy in the local
density of states near the ends of the wire. This zero-energy peak has
qualitative similarities to the claimed signature of a Majorana mode observed
in the aforementioned experiment.
