论文标题
dunkl振荡器在非稳定曲率空间上：具有反射的精确溶解量子模型
The Dunkl oscillator on a space of nonconstant curvature: an exactly solvable quantum model with reflections
论文作者
论文摘要
我们在n维中介绍了dunkl-darboux III振荡器Hamiltonian，定义为n维dunkl振荡器的$λ-$变形。该变形可以解释为在基础空间上与$λ$相关的非恒定曲率的引入，或者等效地将其视为具有位置依赖性质量函数的DUNKL振荡器。该新的量子模型在任意尺寸n中被证明是可以完全解决的，并且其特征值和特征函数明确呈现。此外，在二维情况下，Darboux III和DUNKL振荡器都可以与恒定的磁场分别耦合，从而产生两个新的可解决的量子系统，在这种量子系统中，可以阐明依赖位置依赖性质量的质量以及dunkl衍生物对地产水平的结构的影响。最后，整个2D dunkl-darboux III振荡器与磁场结合，并显示出确切的可解决的哈密顿量，其中$λ$变形与磁场之间的相互作用明确说明了。
We introduce the Dunkl-Darboux III oscillator Hamiltonian in N dimensions, defined as a $λ-$deformation of the N-dimensional Dunkl oscillator. This deformation can be interpreted either as the introduction of a non-constant curvature related to $λ$ on the underlying space or, equivalently, as a Dunkl oscillator with a position-dependent mass function. This new quantum model is shown to be exactly solvable in arbitrary dimension N, and its eigenvalues and eigenfunctions are explicitly presented. Moreover, it is shown that in the two-dimensional case both the Darboux III and the Dunkl oscillators can be separately coupled with a constant magnetic field, thus giving rise to two new exactly solvable quantum systems in which the effect of a position-dependent mass and the Dunkl derivatives on the structure of the Landau levels can be explicitly studied. Finally, the whole 2D Dunkl-Darboux III oscillator is coupled with the magnetic field and shown to define an exactly solvable Hamiltonian, where the interplay between the $λ$-deformation and the magnetic field is explicitly illustrated.
