  We formulate the three-body problem in one dimension in terms of the
(Faddeev-type) integral equation approach. As an application, we develop a
spinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in one
dimension. Using simple two-body potentials that reproduce the deuteron
binding, we obtain that the three-body system binds at about 7.5 MeV. We then
consider two types of residual pionic corrections in the dynamical equation;
one related to the 2PI-exchange three-body diagram, the other to the
1PI-exchange three-body diagram. We find that the first contribution can
produce an additional binding effect of about 0.9 MeV. The second term produces
smaller binding effects, which are, however, dependent on the uncertainty in
the off-shell extrapolation of the two-body t-matrix. This presents interesting
analogies with what occurs in three dimensions. The paper also discusses the
general three-particle quantum scattering problem, for motion restricted to the
full line.
