  The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic
quantum theory is investigated. It is shown that the time evolution exhibits
three different characteristics, depending on the values of the parameters of
the Hamiltonian. When energy eigenvalues are real, the evolution is either
isomorphic to that of a complex Hermitian theory on a spherical state space, or
else it remains unitary along an open orbit on a hyperbolic state space. When
energy eigenvalues form a complex conjugate pair, the orbit of the time
evolution closes again even though the state space is hyperbolic.
