New $q-$Hermite polynomials: characterization, operator algebra and associated coherent states
Mathematical Physics
2013-10-07 v1 math.MP
Abstract
This paper addresses a construction of new Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self-adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem.
Cite
@article{arxiv.1310.1280,
title = {New $q-$Hermite polynomials: characterization, operator algebra and associated coherent states},
author = {Won Sang Chung and Mahouton Norbert Hounkonnou and Arjika Sama},
journal= {arXiv preprint arXiv:1310.1280},
year = {2013}
}