Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions

IF 1.3 4区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY
S. Hassanabadi, J. Kříž, B. C. Lütfüoğlu, W. S. Chung, P. Sedaghatnia, H. Hassanabadi
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引用次数: 0

Abstract

The recent generalization of the Dunkl operator, incorporating six parameters, offers a refined approach to bridging theoretical models and experimental observations. In this study, we apply the fully generalized Dunkl derivatives to solve two cornerstone quantum mechanical problems-the harmonic oscillator and the Coulomb potential-in the non-relativistic context. Our analysis begins with the systems formulated in two-dimensional Cartesian coordinates, followed by a transition to polar coordinates to achieve angular solutions. For the radial component, we identify a required constraint that reduces the set of Wigner parameters by one. This leads to the determination of the radial eigenfunctions and the corresponding energy spectra for both systems, all within the non-relativistic context. Our analysis reveals that the Wigner parameters significantly influence the probability densities, altering the localization of the particle within the potential and highlighting the role of parity in shaping the radial distribution.

二维谐波和库仑势的广义Dunkl-Schrödinger方程的解
最近对Dunkl算子的推广,包括六个参数,提供了一个完善的方法来连接理论模型和实验观察。在本研究中,我们应用完全广义的Dunkl导数来解决非相对论背景下的两个基础量子力学问题——谐振子和库仑势。我们的分析开始于在二维笛卡尔坐标系中表述的系统,然后过渡到极坐标以获得角解。对于径向分量,我们确定了一个所需的约束,将Wigner参数集减少一个。这导致了两个系统的径向本征函数和相应的能谱的确定,所有这些都在非相对论的背景下。我们的分析表明,Wigner参数显著地影响了概率密度,改变了粒子在势内的定位,并突出了宇称在形成径向分布中的作用。
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来源期刊
CiteScore
2.50
自引率
21.40%
发文量
258
审稿时长
3.3 months
期刊介绍: International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.
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