  The breakdown of Ehrenfest's theorem imposes serious limitations on
quaternionic quantum mechanics (QQM). In order to determine the conditions in
which the theorem is valid, we examined the conservation of the probability
density, the expectation value and the classical limit for a non-anti-hermitian
formulation of QQM. The results also indicated that the non-anti-hermitian
quaternionic theory is related to non-hermitian quantum mechanics, and thus the
physical problems described with both of the theories should be related.
