  We investigate potential scattering and tunneling dynamics of a particle
wavepacket evolving according to the relativistic Schr\"odinger equation (also
known as the Salpeter equation). The tunneling properties of the Salpeter
equation differ from those of the standard relativistic wave equations (such as
the Klein-Gordon or Dirac equations). In particular, the tunneling solutions
must be found by working in momentum space, given that the equation in
configuration space contains a pseudo-differential operator. The resulting
integral equations are derived and solved numerically for wavepackets
scattering on model potential barriers. The solutions are characterized by the
absence of Klein tunneling and an effect of the potential on the fraction of
the transmitted wavepacket that propagates outside the light cone, a feature
that has in the past been well-studied only for free propagation.
