  Here we present a simple extension to the age-old Kronig-Penney model, which
is made to be bipartite by varying either the scatterer separations or the
potential heights. In doing so, chiral (sublattice) symmetry can be introduced.
When such a symmetry is present, topologically protected edge states are seen
to exist. The solution proceeds through the conventional scattering formalism
used to study the Kronig-Penney model, which does not require further
tight-binding approximations or mapping into a Su-Schrieffer-Heeger model. The
topological invariant for this specific system is found to be the winding of
the reflection coefficient, ultimately linked to the system wavefunction. The
solution of such a simple and illustrative 1D problem, whose topological
content is extracted without requiring further tight-binding approximations,
represents the novel aspect of our paper. The cases in which chiral symmetry is
absent are then seen to not host topologically protected edge states, as
verified by the behaviour of the reflection coefficient and the absence of
winding.
