Supersymmetric Wigner-Dunkl quantum mechanicsopen access
- Dong, Shi-Hai; Chung, Won Sang; Junker, Georg; Hassanabadi, Hassan
- Issue Date
- Supersymmetric; Wigner-Dunklquantum; Deformedquantummechanics
- RESULTS IN PHYSICS, v.39
- Journal Title
- RESULTS IN PHYSICS
- 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
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- 자연과학대학 > 물리학과 > Journal Articles
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