Generalized imaginary units in quantum mechanics

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.