Supersymmetric Quesne-Dunkl Quantum Mechanics on Radial Lines
Year: 2024
Type: article
Abstract: 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.
Source: Symmetry
DOI: 10.3390/sym16111508
Author: Fethi Bouzeffour
Institution: King Saud University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
Funder: King Saud University
OpenAlex ID: W4404248563