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.

中文翻译：

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一维 Dirac-Dunkl 振荡器的代数方法

我们通过用 Dunkl 导数改变标准导数来扩展 (1 + 1) 维 Dirac-Moshinsky 振荡器。我们以一般的方式证明，对于狄拉克-邓克尔振子奇偶不变，一个旋量分量必须是偶数，而另一个旋量分量必须是奇数，反之亦然。我们将每个旋量分量的微分方程解耦，并在其中一个函数为偶数而另一个函数为奇数的情况下引入适当的 su(1, 1) 代数实现。利用su(1, 1)不可约表示理论得到本征函数和能谱。最后，通过将 Dunkl 参数设置为 vanish，我们表明我们的结果减少到标准 Dirac-Moshinsky 振荡器的结果。