${\theta}(\hat{x},\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space
Abstract
This work addresses a deformation of the harmonic oscillator in a phase space. Specifically, it concerns a quantum mechanics of the harmonic oscillator based on a noncanonical commutation relation depending on the phase space coordinates. A reformulation of this deformation is considered in terms of a deformation allowing to easily deduce the energy spectrum of the induced deformed harmonic oscillator. Then, it is proved that the deformed position and momentum operators admit a one-parameter family of self-adjoint extensions. These operators engender new families of deformed Hermite polynomials generalizing usual Hermite polynomials. Relevant matrix elements are computed. Finally, a algebra representation of the considered deformation is investigated and discussed.
Keywords
Cite
@article{arxiv.1211.0308,
title = {${\theta}(\hat{x},\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space},
author = {M. N. Hounkonnou and D. Ousmane Samary and E. Baloitcha and S. Arjika},
journal= {arXiv preprint arXiv:1211.0308},
year = {2014}
}
Comments
9 pages