  The Lee-Friedrichs model has been very useful in the study of
decay-scattering systems in the framework of complex quantum mechanics. Since
it is exactly soluble, the analytic structure of the amplitudes can be
explicitly studied. It is shown in this paper that a similar model, which is
also exactly soluble, can be constructed in quaternionic quantum mechanics. The
problem of the decay of an unstable system is treated here. The use of the
Laplace transform, involving quaternion-valued analytic functions of a variable
with values in a complex subalgebra of the quaternion algebra, makes the
analytic properties of the solution apparent; some analysis is given of the
dominating structure in the analytic continuation to the lower half plane. A
study of the corresponding scattering system will be given in a succeeding
paper.
