  When two non-relativistic particles scatter in one dimension, they can become
entangled. This entanglement process is constrained by the symmetries of the
scattering system and the boundary conditions on the incoming state. Applying
these constraints, three different mechanisms of entanglement can be
identified: the superposition of reflected and transmitted modes, momentum
correlations of the reflected mode due to inversion of the relative momentum,
and momentum correlations in the transmitted and reflected modes due to
dependence of the scattering amplitude on the relative momentum. We consider
three standard potentials, the hard core, Dirac delta, and double Dirac delta,
and show that the relative importance of these mechanisms depends on the
interaction and on the properties of the incoming wave function. We find that
even when the momenta distributions of the incoming articles are sharply
peaked, entanglement due to the momentum correlations generated by reflection
can be quite large for particles with unequal mass.
