  We address two questions regarding square-well potentials from a didactic
perspective. The first question concerns whether or not the justification of
the standard a priori omission of the potential's vertical segments in the
analysis of the eigenvalue problem is licit. The detour we follow to find out
the answer considers a trapezoidal potential, includes the solution, analytical
and numerical, of the corresponding eigenvalue problem and then analyzes the
behavior of that solution in the limit when the slope of the trapezoidal
potential's ramps becomes vertical. The second question, obviously linked to
the first one, pertains whether or not eigenfunction's and its first
derivative's continuity at the potential's jump points is justified as a priori
assumption to kick-off the solution process, as it is standardly accepted in
textbook approaches to the potential's eigenvalue problem.
