论文标题
一维dirac-dunkl振荡器的代数方法
Algebraic approach for the one-dimensional Dirac-Dunkl oscillator
论文作者
论文摘要
我们通过通过DUNKL衍生品更改标准导数来扩展$（1+1）$ -Dimensional Dirac-Moshinsky振荡器。我们以一种一般的方式证明，对于Dirac-Dunkl振荡器是奇偶校验不变的，旋转器组件之一必须是均匀的，而另一个旋转组件必须是奇怪的，反之亦然。我们将每个旋转器组件的微分方程分离，并引入适当的$ su（1,1）$代数实现，当这些功能之一均匀并且另一个函数奇怪时。使用$ su（1,1）$不可约代表理论获得了本征函数和能量谱。最后，通过将DUNKL参数设置为消失，我们表明我们的结果减少了标准的Dirac-Moshinsky振荡器。
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.
