  We study the evolution of a single-particle wave function during the
collision of a one dimensional potential well by another well, which can be
regarded as a simple model for the problem of the scattering of a one-neutron
halo nucleus by another nucleus. This constitutes an effective three-body
problem, whose solution in three dimensions can be extremely complicated,
particularly when breakup and rearrangement channels are to be considered. Our
one-dimensional model provides the essential three-body nature of this problem,
and allows for a much simpler application and assessment of different methods
of solution. To simplify further the problem, we assume that the potential well
representing the projectile moves according to a predetermined classical
trajectory, although the internal motion of the "valence" particle is treated
fully quantum-mechanically. This corresponds to a semiclassical approach of the
scattering problem. Different approaches are investigated to understand the
dynamics involving one-body halo-like systems: the "exact" time-dependent
solution of the Schr\"odinger equation is compared to a numerical
continuum-discretized coupled-channels (CC) calculation presenting various
model cases including different reaction channels. This framework allows us to
discuss the reaction mechanism and the role of continuum, whose inclusion in
the CC calculation results to be crucial to reproduce the "exact" solution,
even when the initial and final states are well bound. We also link each
dynamical situation with analogous problem solved in a three dimensional (3D)
CC framework, discussing the main challenges experienced in the usual 3D
models.
