We introduce the Dunkl–Klein–Gordon (DKG) equation in 2D by changing the standard partial derivatives by the Dunkl derivatives in the standard Klein–Gordon (KG) equation. We show that the generalization with Dunkl derivative of the z-component of the angular momentum is what allows the separation of variables of the DKG equation. Then, we compute the energy spectrum and eigenfunctions of the DKG equations for the 2D Coulomb potential and the Klein–Gordon oscillator analytically and from an su(1, 1) algebraic point of view. Finally, we show that if the parameters of the Dunkl derivative vanish, the obtained results suitably reduce to those reported in the literature for these 2D problems.

中文翻译：

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二维 Dunkl-Klein-Gordon 方程的精确解：库仑势和 Klein-Gordon 振子

我们通过将标准偏导数更改为标准 Klein-Gordon (KG) 方程中的 Dunkl 导数，在 2D 中引入 Dunkl-Klein-Gordon (DKG) 方程。我们证明了用 Dunkl 导数的泛化z- 角动量的分量允许分离 DKG 方程的变量。然后，我们从 su(1, 1) 代数的角度分析计算二维库仑势和 Klein-Gordon 振子的 DKG 方程的能谱和特征函数。最后，我们表明，如果 Dunkl 导数的参数消失，则获得的结果适当地减少到文献中针对这些 2D 问题报告的结果。