AI 中文总结
本文利用 Schrödinger 分解构造 su(1,1) 代数，求解二维 Dunkl--Pauli 方程在磁场中的精确解，揭示其动力学对称性及宇称依赖的径向呼吸行为。
AI 中文摘要
我们在代数框架内研究自旋-1/2 粒子在外部磁场中的二维 Dunkl--Pauli 方程。尽管先前的研究已提供 Dunkl--Pauli 系统的精确解，但其潜在的动力学对称性和代数结构在很大程度上仍未探索。通过采用 Schrödinger 分解，我们构造了 $\mathfrak{su}(1,1)$ 代数的生成元，并建立了径向扇区的相关对称性。利用不可约酉表示推导出能量谱，并解析地获得了相应的 Sturmian 径向基。此外，构造了 $\mathrm{SU}(1,1)$ 相干态并分析了其时间演化，揭示了特征性的径向呼吸行为。结果表明，Dunkl 变形在保持系统潜在代数动力学的同时，引入了宇称依赖的空间结构修正。
英文摘要
We investigate the two-dimensional Dunkl--Pauli equation for a spin--$1/2$ particle in the presence of an external magnetic field within an algebraic framework. While previous studies have provided exact solutions of the Dunkl--Pauli system, its underlying dynamical symmetry and algebraic structure remain largely unexplored. By employing Schrödinger factorization, we construct the generators of the $\mathfrak{su}(1,1)$ algebra and establish the associated symmetry of the radial sector. The energy spectrum is derived using irreducible unitary representations, and the corresponding Sturmian radial basis is obtained analytically. Furthermore, $\mathrm{SU}(1,1)$ coherent states are constructed and their time evolution is analyzed, revealing a characteristic radial breathing behavior. The results show that the Dunkl deformation introduces parity-dependent modifications in the spatial structure of the system while preserving its underlying algebraic dynamics.
Journal refPhys. Scr. 101 (2026) 215101
