  The properties of quantum mechanics with a discrete phase space are studied.
The minimum uncertainty states are found, and these states become the Gaussian
wave packets in the continuum limit. With a suitably chosen Hamiltonian that
gives free particle motion in the continuum limit, it is found that full or
approximate periodic time evolution can result. This represents an example of
revivals of wave packets that in the continuum limit is the familiar free
particle motion on a line. Finally we examine the uncertainty principle for
discrete phase space and obtain the correction terms to the continuum case.
