Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications

IF 1.8 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Few-Body Systems Pub Date : 2025-06-27 DOI:10.1007/s00601-025-01999-5

B. Hamil, B. C. Lütfüoğlu, A. N. Ikot, U. S. Okorie

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引用次数: 0

Abstract

In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator–which introduces reflection symmetry–we construct a deformed Schrödinger equation and obtain exact analytical solutions using the Pekeris approximation. The resulting energy spectrum and wavefunctions reveal how Dunkl parameters alter the effective potential and vibrational states. The model is applied to several diatomic molecules, including \(\hbox {H}_2\), HCl, and \(\hbox {I}_2\), illustrating the impact of symmetry deformation on energy spectra. We also compute thermodynamic functions including the partition function, free energy, internal energy, entropy, and specific heat. The analysis shows that the Dunkl deformation induces distinct thermal behavior and offers a tunable approach to molecular modeling. These results highlight the potential of the Dunkl formalism as a useful tool for extending conventional quantum models and for exploring symmetry-deformed systems in molecular physics and quantum thermodynamics.

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Dunkl形式中摩尔斯势的光谱和热分析：解析近似和应用

在这项工作中，我们在邓克尔量子力学的框架内研究了受莫尔斯势影响的粒子的量子动力学。利用引入反射对称性的Dunkl导数算子，构造了一个变形Schrödinger方程，并利用Pekeris近似得到了精确解析解。所得的能谱和波函数揭示了Dunkl参数如何改变有效势态和振动态。该模型应用于若干双原子分子，包括\(\hbox {H}_2\)、HCl和\(\hbox {I}_2\)，说明了对称变形对能谱的影响。我们也计算热力学函数，包括配分函数、自由能、内能、熵和比热。分析表明，Dunkl变形引起了不同的热行为，为分子建模提供了一种可调的方法。这些结果突出了Dunkl形式化作为扩展传统量子模型和探索分子物理和量子热力学中对称变形系统的有用工具的潜力。

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来源期刊

Few-Body Systems 物理-物理：综合

CiteScore

2.90

自引率

18.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Few-Body Systems presents original research work – experimental, theoretical and computational – investigating the behavior of any classical or quantum system consisting of a small number of well-defined constituent structures. The focus is on the research methods, properties, and results characteristic of few-body systems. Examples of few-body systems range from few-quark states, light nuclear and hadronic systems; few-electron atomic systems and small molecules; and specific systems in condensed matter and surface physics (such as quantum dots and highly correlated trapped systems), up to and including large-scale celestial structures. Systems for which an equivalent one-body description is available or can be designed, and large systems for which specific many-body methods are needed are outside the scope of the journal. The journal is devoted to the publication of all aspects of few-body systems research and applications. While concentrating on few-body systems well-suited to rigorous solutions, the journal also encourages interdisciplinary contributions that foster common approaches and insights, introduce and benchmark the use of novel tools (e.g. machine learning) and develop relevant applications (e.g. few-body aspects in quantum technologies).