发表机构
Khalifa University of Science and Technology; Center for Cyber-Physical Systems (C2PS), Khalifa University of Science and Technology（哈利法科学技术大学; 哈利法科学技术大学网络物理系统中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对共线电磁场中的带电粒子，提出基于三对角表示方法的径向框架，在弱磁场近似下推导解析谱并借助Galerkin模拟验证，提供场修正势的基准模型。
AI 中文摘要
我们开发了一个有效的径向框架，用于分析带电无自旋粒子在共线电场和磁场中的新型场修正势函数。在弱磁场近似下，我们在显式小量条件$\ll \Delta E$下忽略抗磁项和其他角投影，其中$E$是电场，并在球坐标中将角因子替换为$C=\cos\theta$。由此得到的方程因此是一个场对齐的径向模型，其有效性仅限于角向局域态。在此设置下，我们应用三对角表示方法的间接模式（或搜索模式），在Laguerre和Jacobi基中进行分析。在Laguerre基中，三对角约束生成线性加反比和线性加二次径向势，系数递推关系与Meixner--Pollaczek和Meixner多项式型结构相关联，从而得到解析谱和展开波函数。在Jacobi基中，将径向半直线映射到有限区间会产生奇异约束有效势和一个三项递推关系，该递推关系通过截断广义特征值问题处理。该公式为场修正势函数提供了解析和数值上可处理的基准模型，同时明确给出了假设、参数限制、端点行为和收敛性测试。在当前模型下获得的所有能谱公式都是新的，并且在使用Laguerre基和Jacobi基时分别以解析和数值方式与磁场耦合。
英文摘要
We develop an effective radial framework for analyzing new field-modified potential function of a charged spinless particle in collinear electric and magnetic fields. Using the weak- magnetic field approximation, we neglect the diamagnetic term and other angular projections under an explicit smallness condition $\ll ΔE$, where $E$ is the electric field, and the replacement of the angular factor by $C=\cosθ$ in the spherical coordinates. The resulting equation is therefore a field-aligned radial model whose validity is limited to angularly localized states. Within this setting, we apply the indirect mode (or search mode) of Tridiagonal representation approach in the Laguerre and Jacobi bases. In the Laguerre basis, the tridiagonal constraint generates linear-plus-inverse and linear-plus-quadratic radial potentials, and the coefficient recurrences are connected with Meixner--Pollaczek and Meixner polynomial type structures, therefore yielding the analytic spectra and expansion wavefunctions. In the Jacobi basis, the mapping of the radial half-line to a finite interval produces a singular confining effective potential and a three-term recurrence that is treated through a truncated generalized eigenvalue problem. The formulation provides analytically and numerically tractable benchmark models for field-modified potential functions, while keeping the assumptions, parameter restrictions, endpoint behavior, and convergence tests explicit. All energy spectra formulae obtained under the present models are new and are coupled with magnetic fields analytically and numerically when using the Laguerre bases and the Jacobi bases respectively.
Comments21 pages, 11 figures, 1 table
