Wave Packets in Discrete Quantum Phase Space

TL;DR

This paper explores quantum mechanics in discrete phase space, identifying minimum uncertainty states, wave packet revivals, and corrections to the uncertainty principle, bridging discrete and continuum quantum behaviors.

Contribution

It introduces the properties of wave packets and their dynamics in discrete quantum phase space, including revival phenomena and uncertainty principle modifications.

Findings

Minimum uncertainty states become Gaussian wave packets in the continuum limit

Wave packets can exhibit revivals under suitable Hamiltonians

Corrections to the uncertainty principle are derived for discrete 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.