Wave Packets in Discrete Quantum Phase Space

Abstract

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.