标题： 爱因斯坦-麦克斯韦-Λ时空中的PDM相对论量子振子 显示英文标题

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

摘要： 在本分析中，我们研究了在位置依赖质量（PDM）系统中的量子振子场的动力学，该系统位于爱因斯坦-麦克斯韦时空内，并包含一个非零的宇宙学常数。磁场沿对称轴方向对齐。为了分析PDM量子振子场，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-戈登方程来修改克莱因-戈登方程，其中四矢量由$X_{\mu}=(0, r, 0, 0)$，$\mathcal{F}_{\mu}=(0, \mathcal{F}_r, 0, 0)$与$\mathcal{F}_r=\frac{f'(r)}{4\,f(r)}$定义，而$\eta$是振子质量频率。 相对论性修正克莱因-戈登方程的径向波方程被推导出来，并随后针对两种不同的情况求解：(i)$f(r)=e^{\frac{1}{2}\,\alpha\,r^2}$，以及 (ii)$f(r)=r^{\beta}$，其中$\alpha \geq 0, \beta \geq 0$。 结果得到的量子振子场的能量本征值和波函数被证明受到宇宙学常数和几何拓扑参数的影响，这些因素打破了能量谱的简并性。 此外，与在平坦空间背景中得出的结果相比，我们观察到能量本征值和波函数有显著的修改。 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.