Generalized discrete q-Hermite II polynomials and q-deformed oscillator
Kamel Mezlini
TL;DR
This paper introduces a new realization of a q-deformed algebra using generalized discrete q-Hermite II polynomials, constructing wave functions and q-coherent states to advance understanding of q-deformed oscillators.
Contribution
It provides an explicit realization of q-deformed Calogero-Vasiliev algebra with generators as q-difference operators linked to new generalized discrete q-Hermite II polynomials.
Findings
Explicit realization of q-deformed algebra
Construction of wave functions and q-coherent states
Connection to generalized discrete q-Hermite II polynomials
Abstract
In this paper, we present an explicit realization of q-deformed Calogero-Vasiliev algebra whose generators are first-order q-difference operators related to the generalized discrete q-Hermite II polynomials recently introduced in [13]. Furthermore, we construct the wave functions and we determine the q-coherent states.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra