2008/11/06 by Jang Young Bang, M. S. Berger, Micheal S Berger · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical limit #Classical mechanics #Free particle #Gaussian #Hamiltonian (control theory) #Limit (mathematics) #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Phase space #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum limit #Quantum mechanics #Statistical physics #Wave packet #gr-qc #quant-ph
paper · pdf · doi:10.1103/physreva.80.022105
published as Phys.Rev.A80:022105,2009 · 19 pages, 6 figures
arxiv created 2008/11/06 · openalex publication_date 2009/08/04 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.