  We review the analytic results for the phase shifts delta_{l}(k) in
non-relativistic scattering from a spherical well. The conditions for the
existence of resonances are established in terms of time-delays. Resonances are
shown to exist for p-waves (and higher angular momenta) but not for s-waves.
These resonances occur when the potential is not quite strong enough to support
a bound p-wave of zero energy. We then examine relativistic scattering by
spherical wells and barriers in the Dirac equation. In contrast to the
non-relativistic situation, s-waves are now seen to possess resonances in
scattering from both wells and barriers. When s-wave resonances occur for
scattering from a well, the potential is not quite strong enough to support a
zero momentum s-wave solution at E = m. Resonances resulting from scattering
from a barrier can be explained in terms of the `crossing' theorem linking
s-wave scattering from barriers to p-wave scattering from wells. A numerical
procedure to extract phase shifts for general short range potentials is
introduced and illustrated by considering relativistic scattering from a
Gaussian potential well and barrier.
