Supersymmetric Wigner–Dunkl quantum mechanics

Dong, Shi‐Hai; Chung, Won Sang; Junker, Georg; Hassanabadi, Hassan

doi:10.1016/j.rinp.2022.105664

Cited by 14 publications

(9 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…in Ref. [24]. On the other hand, starting with the generalized Dunkl supersymmetric quantum mechanics operators…”

Section: The Dunkl-fokker-planck Equation and Wigner-dunkl Supersymmetrymentioning

confidence: 99%

The Dunkl-Fokker-Planck Equation in 1+1 Dimensions

Esteves,

Guillén,

Merino

2024

Preprint

View full text Add to dashboard Cite

By replacing the spatial derivative with the Dunkl derivative, we generalize the Fokker-Planck equation in (1+1) dimensions. We obtain the Dunkl-Fokker-Planck eigenvalues equation and solve it for the harmonic oscillator plus a centrifugal-type potential. Furthermore, when the drift function is odd, we reduce our results to those of the recently developed Wigner-Dunkl supersymmetry. PACS: 02.30.Ik, 02.30.Jr, 03.65.Ge, 05.10.Gg

show abstract

“…in Ref. [24]. On the other hand, starting with the generalized Dunkl supersymmetric quantum mechanics operators…”

Section: The Dunkl-fokker-planck Equation and Wigner-dunkl Supersymmetrymentioning

confidence: 99%

The Dunkl-Fokker-Planck Equation in 1+1 Dimensions

Esteves,

Guillén,

Merino

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Nonlinear phenomena exist widely in nature, and nonlinear partial differential equations (NLPDEs) are indispensable tools to describe the nonlinear phenomena. Nowadays, NLPDEs are widely used in water waves [1], elastic mechanics [2], quantum mechanics [3], plasma physics [4,5], nonlinear optics [6,7], communication engineering [8,9], biomedicine [10] and other fields [11][12][13]. It is well known that in some real-world problems, NLPDEs with variable coefficients provide a more realistic perspective on the inhomogeneities of media and non-uniformities of boundaries in comparison than NLPDEs with constant coefficients, and have applications in various fields such as optical fibers [14], propagations of wave and rogue waves [15], and various other physical systems [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Various nonlinear characteristics of breather/rogue waves and controllable interaction phenomena for a new KdV equation with variable coeffcients

Lv,

Yue,

Zhang

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

In this paper, we investigate and analyze various nonlinear phenomena of a new (2+1)-dimensional KdV equation with variable coefficients, and successfully obtain breather/rogue wave solutions and interaction solutions of the KdV equation by using the bilinear neural network method and symmetry transformation. Subsequently, we analyze the dynamical characteristics and evolution process of these obtained solutions through the 3-D animations, and find a series of interesting nonlinear phenomena concerning breather/rogue waves, such as fission, regeneration, annihilation, collision, and controllable interaction phenomena on nonzero backgrounds. This paper provides a more intuitive understanding for the nonlinear phenomena of these obtained solutions, and these nonlinear phenomena have potential application value in fluid dynamics, elastic mechanics and other fields of nonlinear science.

show abstract

“…One may quote, for instance, the Dunkl oscillators in one, two, and three dimensions [20][21][22][23][24], the Dunkl-Coulomb problem in two and three dimensions [25][26][27], as well as the one-dimensional infinite [28] and finite [29] square wells. Coherent states [30], a generalization of shape invariance in supersymmetric quantum mechanics [31], Dunkl derivatives with two and three parameters [32,33], and some relativistic systems [34,35] have also been investigated.…”

Section: Introductionmentioning

confidence: 99%

Rationally-extended Dunkl oscillator on the line

Quesne

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

It is shown that the extensions of exactly-solvable quantum mechanical problems connected with the replacement of ordinary derivatives by Dunkl ones and with that of classical orthogonal polynomials by exceptional orthogonal ones can be easily combined. For such a purpose, the example of the Dunkl oscillator on the line is considered and three diﬀerent types of rationally-extended Dunkl oscillators are constructed. The corresponding wavefunctions are expressed in terms of exceptional orthogonal generalized Hermite polynomials, deﬁned in terms of the three diﬀerent types of Xm-Laguerre exceptional orthogonal polynomials. Furthermore, the extended Dunkl oscillator Hamiltonians are shown to be expressible in terms of some extended Dunkl derivatives and some anharmonic oscillator potentials.

show abstract

Supersymmetric Wigner–Dunkl quantum mechanics

Cited by 14 publications

References 18 publications

The Dunkl-Fokker-Planck Equation in 1+1 Dimensions

The Dunkl-Fokker-Planck Equation in 1+1 Dimensions

Various nonlinear characteristics of breather/rogue waves and controllable interaction phenomena for a new KdV equation with variable coeffcients

Rationally-extended Dunkl oscillator on the line

Contact Info

Product

Resources

About