Exact Solutions of the Dunkl--Pauli Equation in the Presence of a Magnetic Field from an su(1,1) Algebraic Approach

Abstract: 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.