  We introduce a simple quantum mechanical model in which time and space are
discrete and periodic. These features avoid the complications related to
continuous-spectrum operators and infinite-norm states. The model provides a
tool for discussing the probabilistic interpretation of generally-covariant
quantum systems, without the confusion generated by spurious infinities. We use
the model to illustrate the formalism of general-relativistic quantum
mechanics, and to test the definition of multiple-event probability introduced
in a companion paper. We consider a version of the model with unitary
time-evolution and a version without unitary time-evolution
