  We study the bound-state solutions of vanishing angular momentum in a
quaternionic spherical square-well potential of finite depth. As in the
standard quantum mechanics, such solutions occur for discrete values of
energies. At first glance, it seems that the continuity conditions impose a
very restrictive constraint on the energy eigenvalues and, consequently, no
bound states was expected for energy values below the pure quaternionic
potential. Nevertheless, a careful analysis shows that pure quaternionic
potentials do not remove bound states. It is also interesting to compare these
new solutions with the bound state solutions of the trial-complex potential.
The study presented in this paper represents a preliminary step towards a full
understanding of the role that quaternionic potentials could play in quantum
mechanics. Of particular interest for the authors it is the analysis of
confined wave packets and tunnelling times in this new formulation of quantum
theory.
