  In looking for qualitative differences between quaternionic and complex
formulations of quantum physical theories, we provide a detailed discussion of
the behavior of a wave packet in presence of a quaternionic time-independent
potential step. In this paper, we restrict our attention to diffusion
phenomena. For the group velocity of the wave packet moving in the potential
region and for the reflection and transmission times, the study shows a
striking difference between the complex and quaternionic formulations which
could be matter of further theoretical discussions and could represent the
starting point for a possible experimental investigation.
