标题： 爱因斯坦-麦克斯韦-Λ时空中的相对论量子振荡器 显示英文标题

标题： PDM relativistic quantum oscillator in Einstein-Maxwell-Lambda space-time

摘要： 在这项分析中，我们研究了在爱因斯坦-麦克斯韦时空背景下具有位置相关质量（PDM）系统的量子振荡场的动力学，并考虑了一个非零宇宙学常数。磁场沿着对称轴方向排列。 为了分析PDM量子振荡场，我们通过将四动量矢量$p_{\mu} \to \Big(p_{\mu}+i\,\eta\,X_{\mu}+i\,\mathcal{F}_{\mu}\Big)$代入克莱因-戈登方程来修改该方程，其中四矢量由$X_{\mu}=(0, r, 0, 0)$，$\mathcal{F}_{\mu}=(0, \mathcal{F}_r, 0, 0)$和$\mathcal{F}_r=\frac{f'(r)}{4\,f(r)}$定义，而$\eta$是振荡器频率。 我们推导了相对论修正Klein-Gordon方程的径向波动方程，并随后针对两种不同情形求解：(i) $f(r)=e^{\frac{1}{2}\,\alpha\,r^2}$，以及(ii) $f(r)=r^{\beta}$，其中 $\alpha \geq 0, \beta \geq 0$。 量子振荡场的能量水平和波函数结果表明，它们受到宇宙常数以及破坏能级简并的几何拓扑参数的影响。 此外，与平坦空间背景下的结果相比，我们观察到能量水平和波函数出现了值得注意的修改。 显示英文摘要

摘要： In this analysis, we study the dynamics of quantum oscillator fields within the context of a position-dependent mass (PDM) system situated in an Einstein-Maxwell space-time, incorporating a non-zero cosmological constant. The magnetic field is aligned along the symmetry axis direction. To analyze PDM quantum oscillator fields, we introduce a modification to the Klein-Gordon equation by substituting the four-momentum vector $p_{\mu} \to \Big(p_{\mu}+i\,\eta\,X_{\mu}+i\,\mathcal{F}_{\mu}\Big)$ into the Klein-Gordon equation, where the four-vector is defibed by $X_{\mu}=(0, r, 0, 0)$, $\mathcal{F}_{\mu}=(0, \mathcal{F}_r, 0, 0)$ with $\mathcal{F}_r=\frac{f'(r)}{4\,f(r)}$, and $\eta$ is the mass oscillator frequency. The radial wave equation for the relativistic modified Klein-Gordon equation is derived and subsequently solved for two distinct cases: (i) $f(r)=e^{\frac{1}{2}\,\alpha\,r^2}$, and (ii) $f(r)=r^{\beta}$, where $\alpha \geq 0, \beta \geq 0$. The resultant energy levels and wave functions for quantum oscillator fields are demonstrated to be influenced by both the cosmological constant and the geometrical topology parameter which breaks the degeneracy of the energy spectrum. Furthermore, we observed noteworthy modifications in the energy levels and wave functions when compared to the results derived in the flat space background.