  Magnetic impurities create in-gap states on superconductors. Recent
experiments explore the topological properties of one-dimensional arrays of
magnetic impurities on superconductors, because in certain regimes p-wave
pairing can be locally induced leading to new topological phases. A by-product
of the new accessible phases is the appearance of zero-energy edge states that
have non-Abelian exchange properties and can be used for topological quantum
computation. Despite the large amount of theory devoted to these systems, most
treatments use approximations that render their applicability limited when
comparing with usual experiments of 1-D impurity arrays on wide-band
superconductors. These approximations either involve tight-binding-like
approximations where the impurity energy scales match the minute energy scale
of the superconducting gap and are many times unrealistic, or they assume
strongly-bound in-gap states. Here, we present a theory for s-wave
superconductors based on a wide-band normal metal, with any possible energy
scale for the magnetic impurities. The theory is based on free-electron Green's
functions. We include Rashba coupling and compare with recent experimental
results, permitting us to analyze the topological phases and the experimental
edge states. The infinite-chain properties can be analytically obtained, giving
us a way to compare with finite-chain calculations. We show that it is possible
to converge to the infinite limit by doing finite numerical calculation, paving
the way for numerical calculations not based on analytical Green's functions.
