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.

19 pages, 6 figures

References in corpus (3)

• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• Quantum Mechanics and the Generalized Uncertainty Principle

Cited by in corpus (6)

• Operator Spreading in Quantum Maps
• Free particle wavefunction in light of the minimum-length deformed quantum mechanics and some of its phenomenological implications
• Theoretical formulation of finite-dimensional discrete phase spaces: II. On the uncertainty principle for Schwinger unitary operators
• Properties of finite Gaussians and the discrete-continuous transition
• Conceptual inconsistencies in finite-dimensional quantum and classical mechanics
• Properties of a Discrete Quantum Field Theory