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

Supersymmetric Wigner-Dunkl Quantum Mechanics

Shi-Hai Dong, Won Sang Chung, Georg Junker, HASSAN HASSANABADI

Published Jan 1, 2022• 0 citations
Publisher
DOI
10.2139/ssrn.4092663

Related papers

Supersymmetric Wigner-Dunkl Quantum Mechanics

Shi-Hai Dong, Won Sang Chung, Georg Junker +1 more

•Jan 1, 2022•0 citations

Fractional supersymmetric quantum mechanics as a set of replicas of ordinary supersymmetric quantum mechanics

Mohammed Daoud A, M. Kibler

arXiv:math-ph/0312019•Physics Letters A•Dec 23, 2003•34 citations

Supersymmetric Wigner–Dunkl quantum mechanics

Shi‐Hai Dong, Won Sang Chung, Georg Junker +1 more

Wigner–Dunkl quantum mechanics can be viewed as deformed quantum mechanics, where the commutator between canonical momentum and position operators contains in addition a reflection operator. In the present work we carry over the general concepts of supersymmetric (SUSY) quantum mechanics to the Wigner–Dunkl quantum formulation. We investigate the SUSY ground states, the SUSY transformations and introduce a generalized shape invariance allowing for explicit solutions. In this way, exact solutions for a certain class of SUSY potentials can be provided. As example the harmonic oscillator is considered. We also take a look into a singular oscillator model, which does not belong to the shape-invariance class. Nevertheless, exact solutions can be provided, showing the peculiarities of that model in the SUSY Wigner–Dunkl quantum mechanics. A modification of that singular model is presented which restores shape invariance

Results in Physics•Jun 3, 2022•25 citations

Supersymmetric quantum mechanics

M. Kibler, Mohammed Daoud

arXiv:quant-ph/0409169•Annals of Physics•Oct 1, 1983•7 citations

Supersymmetric Quesne-Dunkl Quantum Mechanics on Radial Lines

Fethi Bouzeffour

Quantum deformations offer valuable perspectives into quantum mechanics, particularly by advancing our understanding of symmetry and algebraic structures.The Dunkl oscillator, which integrates Dunkl operators into the harmonic oscillator framework, advances the system’s algebraic properties and opens new approaches for exploring quantum phenomena. Supersymmetric quantum mechanics (SSQM) unifies bosonic and fermionic aspects and facilitates the construction of solvable models using generalized Dunkl operators. This paper introduces a new approach to the Dunkl oscillator, employing a complex reflection operator to deepen the understanding of its connection to Hermite polynomials on radial lines. The results offer new perspectives on the Dunkl oscillator’s algebraic structure and its relevance to SSQM and quantum deformation theory, expanding the potential for discovering solvable quantum models.

Symmetry•Nov 10, 2024•4 citations

Supersymmetric quantum mechanics

Georg Junker

Institute of Physics eBooks•Jan 1, 2019•1 citation
Wigner–Dunkl quantum mechanics can be viewed as deformed quantum mechanics, where the commutator between canonical momentum and position operators contains in addition a reflection operator. In the present work we carry over the general concepts of supersymmetric (SUSY) quantum mechanics to the Wigner–Dunkl quantum formulation. We investigate the SUSY ground states, the SUSY transformations and introduce a generalized shape invariance allowing for explicit solutions. In this way, exact solutions for a certain class of SUSY potentials can be provided. As example the harmonic oscillator is considered. We also take a look into a singular oscillator model, which does not belong to the shape-invariance class. Nevertheless, exact solutions can be provided, showing the peculiarities of that model in the SUSY Wigner–Dunkl quantum mechanics. A modification of that singular model is presented which restores shape invariance
Quantum deformations offer valuable perspectives into quantum mechanics, particularly by advancing our understanding of symmetry and algebraic structures.The Dunkl oscillator, which integrates Dunkl operators into the harmonic oscillator framework, advances the system’s algebraic properties and opens new approaches for exploring quantum phenomena. Supersymmetric quantum mechanics (SSQM) unifies bosonic and fermionic aspects and facilitates the construction of solvable models using generalized Dunkl operators. This paper introduces a new approach to the Dunkl oscillator, employing a complex reflection operator to deepen the understanding of its connection to Hermite polynomials on radial lines. The results offer new perspectives on the Dunkl oscillator’s algebraic structure and its relevance to SSQM and quantum deformation theory, expanding the potential for discovering solvable quantum models.