Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Geometric Methods in Modern Physics

The symmetric q-oscillator algebra: q-coherent states, q-Bargmann–Fock realization and continuous q-Hermite polynomials with 0 < q < 1

Hossein Fakhri, A. Hashemi

Published Dec 20, 2015• 8 citations
Publisher

Abstract

The symmetric [Formula: see text]-analysis is used to construct a type of minimum-uncertainty [Formula: see text]-coherent states in the Fock representation space of the symmetric [Formula: see text]-oscillator ∗-algebra with [Formula: see text]. Then, its corresponding [Formula: see text]-Hermite polynomials are derived by using the [Formula: see text]-Bargmann–Fock realization of the symmetric [Formula: see text]-oscillator algebra.

DOI
10.1142/s0219887816500286

Related papers

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

Hossein Fakhri, S. Elham Mousavigharalari

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

International Journal of Geometric Methods in Modern Physics•Nov 29, 2019•4 citations

The q-Deformed Oscillator Representations and Their Coherent States of the su(1, 1) Algebra

We present various oscillator representations of the q-deformed su(1,1) algebra such as the Holstein-Primakoff, the Dyson, the Fock-Bargmann, the anyonic, and the parabose oscillator representations and discuss their coherent states with the resolution of unity. 1.

•Jan 1, 1997•0 citations

New $q-$Hermite polynomials: characterization, operator algebra and associated coherent states

Won Sang Chung, Mahouton Norbert Hounkonnou, Sama Arjika

This paper addresses a construction of new $q-$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.

arXiv:1310.1280•Oct 4, 2013•1 citation

New q -Hermite polynomials: characterization, operators algebra and associated coherent states

Won Sang Chung, Mahouton Norbert Hounkonnou, Sama Arjika

This paper addresses a construction of new q-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. The phase collapse in a q-deformed boson system is studied.

Fortschritte der Physik•Jan 1, 2015•4 citations

On the role of Hermite-like polynomials in the Fock representations of Gaussian states

Gianfranco L. Pierobon, Gianfranco Cariolaro, G. Dattoli

The expansion of quantum states and operators in terms of Fock states plays a fundamental role in the field of continuous-variable quantum mechanics. In particular, for general single-mode Gaussian operators and Gaussian noisy states, many different approaches have been used in the evaluation of their Fock representation. In this paper, a natural approach has been applied using exclusively the operational properties of the Hermite and Hermite-like polynomials and showing their fundamental role in this field. Closed-form results in terms of polynomials, exponentials, and simple algebraic functions are the major contribution of the paper.

arXiv:1905.10873•Journal of Mathematical Physics•Aug 1, 2021•3 citations

Generalized discrete q-Hermite II polynomials and q-deformed oscillator

Kamel Mezlini

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.

arXiv:1511.08879•Nov 28, 2015•0 citations
The symmetric [Formula: see text]-analysis is used to construct a type of minimum-uncertainty [Formula: see text]-coherent states in the Fock representation space of the symmetric [Formula: see text]-oscillator ∗-algebra with [Formula: see text]. Then, its corresponding [Formula: see text]-Hermite polynomials are derived by using the [Formula: see text]-Bargmann–Fock realization of the symmetric [Formula: see text]-oscillator algebra.
We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.
New q−q-q−Hermite polynomials: characterization, operator algebra and associated coherent states
This paper addresses a construction of new q−q-q−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.
This paper addresses a construction of new q-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. The phase collapse in a q-deformed boson system is studied.
The expansion of quantum states and operators in terms of Fock states plays a fundamental role in the field of continuous-variable quantum mechanics. In particular, for general single-mode Gaussian operators and Gaussian noisy states, many different approaches have been used in the evaluation of their Fock representation. In this paper, a natural approach has been applied using exclusively the operational properties of the Hermite and Hermite-like polynomials and showing their fundamental role in this field. Closed-form results in terms of polynomials, exponentials, and simple algebraic functions are the major contribution of the paper.