Algebraic approach for the one-dimensional Dirac-Dunkl oscillator
| Autor: | R. D. Mota, M. Salazar-Ramírez, D. Ojeda-Guillén, V. D. Granados |
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| Rok vydání: | 2020 |
| Předmět: |
Physics
Quantum Physics Nuclear and High Energy Physics Partial differential equation 010308 nuclear & particles physics Dirac (software) General Physics and Astronomy FOS: Physical sciences Astronomy and Astrophysics Mathematical Physics (math-ph) 01 natural sciences chemistry.chemical_compound symbols.namesake chemistry Dirac equation 0103 physical sciences Lie algebra symbols Relativistic wave equations Algebraic number 010306 general physics Quantum Physics (quant-ph) Mathematical Physics Derivative (chemistry) Mathematical physics |
| DOI: | 10.48550/arxiv.2003.08975 |
| Popis: | We extend the $(1+1)$-dimensional Dirac-Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac-Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate $su(1,1)$ algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the $su(1,1)$ irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator. Comment: 15 pages |
| Databáze: | OpenAIRE |
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