In this letter, we present the exact solution of the three-dimensional Klein–Gordon oscillator on the (anti)-de Sitter spaces, the energy spectrum and the associated wave functions are extracted and the wave functions are expressed according to the Jacobi polynomial. On the other hand, we have investigated the three-dimensional the Klein–Gordon equation with a Coulomb plus scalar potential, we use the perturbation theory to calculate corrections to the spectrum in this framework of the extended uncertainty principle.

中文翻译：

---

存在最小动量不确定性的无自旋相对论粒子

在这封信中，我们提出了三维 Klein-Gordon 振荡器在（反）德西特空间上的精确解，提取了能谱和相关波函数，并根据雅可比多项式表示了波函数。另一方面，我们研究了具有库仑加标量势的三维 Klein-Gordon 方程，我们使用微扰理论来计算扩展不确定性原理框架中的频谱校正。