The Noncommutative Harmonic Oscillator based in Simplectic Representation of Galilei Group
Mathematical Physics
2013-03-14 v2 math.MP
Abstract
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using the group theory approach as a guide a physical consistent theory in phase space is constructed. The state is described by a quasi-probability amplitude that is in association with the Wigner function. The 3D harmonic oscillator and the noncommutative oscillator are studied in phase space as an application, and the Wigner function associated to both cases are determined.
Keywords
Cite
@article{arxiv.1208.6348,
title = {The Noncommutative Harmonic Oscillator based in Simplectic Representation of Galilei Group},
author = {R. G. G. Amorim and S. C. Ulhoa and A. E. Santana},
journal= {arXiv preprint arXiv:1208.6348},
year = {2013}
}
Comments
7 pages,no figures