A new kind of representations on noncommutative phase space
Mathematical Physics
2009-04-03 v1 High Energy Physics - Theory
math.MP
Abstract
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties between degrees of freedom of different coordinate and momentum components. To show their potential applications, we derive explicit expressions of Wigner function and Wigner operator in the new representations, as well as solve exactly a two-dimensional harmonic oscillator on the noncommutative phase plane with both kinetic coupling and elastic coupling.
Cite
@article{arxiv.0902.3782,
title = {A new kind of representations on noncommutative phase space},
author = {Si-Cong Jing and Bing-Sheng Lin},
journal= {arXiv preprint arXiv:0902.3782},
year = {2009}
}