  We develop scattering theory in a non-commutative space defined by a $su(2)$
coordinate algebra. By introducing a positive operator valued measure as a
replacement for strong position measurements, we are able to derive explicit
expressions for the probability current, differential and total cross-sections.
We show that at low incident energies the kinematics of these expressions is
identical to that of commutative scattering theory. The consequences of spacial
non-commutativity are found to be more pronounced at the dynamical level where,
even at low incident energies, the phase shifts of the partial waves can
deviate strongly from commutative results. This is demonstrated for scattering
from a spherical well. The impact of non-commutativity on the well's spectrum
and on the properties of its bound and scattering states are considered in
detail. It is found that for sufficiently large well-depths the potential
effectively becomes repulsive and that the cross-section tends towards that of
hard sphere scattering. This can occur even at low incident energies when the
particle's wave-length inside the well becomes comparable to the
non-commutative length-scale.
