Beginning with the quaternionic generalization of the Schrödinger equation, we present a simple system consisting of two successive square barriers of general (quaternionic) height, and discuss situations in which the predictions of quaternionic quantum mechanics differ from those of the usual complex theory. Specifically, we show that the transmission coefficient may pick up a phase change on reversal of the barrier order. We comment on why this phase change would not necessarily be observed in experiments. Finally, we present a necessary condition for the magnitude of the transmission coefficient to change under reversal of the direction of traversal of the barrier.

• Received 31 March 1992

DOI:https://doi.org/10.1103/PhysRevA.46.3671