  The generalization of the imaginary unit is examined within the instances of
the complex quantum mechanics ($\mathbb C$QM), and of the quaternionic quantum
mechanics ($\mathbb H$QM) as well. Whereas the complex theory describes
non-stationary quantum processes, the quaternionic theory does not admit such
an interpretation, and associates the generalized imaginary unit to a novel
time evolution function. Various possibilities are opened as future directions
for future research.
