  The complex unit appearing in the equations of quantum mechanics is
generalised to a quaternionic structure on spacetime, leading to the
consideration of complex quantum mechanical particles whose dynamical behaviour
is governed by inhomogeneous Dirac and Schr\"{o}dinger equations. Mixing of
hyper-complex components of wavefunctions occurs through their interaction with
potentials dissipative into the extra quaternionic degrees of freedom. An
interferometric experiment is analysed to illustrate the effect.
