标题： 在 Dunkl 形式主义下莫尔斯势的光谱和热分析：解析近似与应用 显示英文标题

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

摘要： 在本工作中，我们研究了在Dunkl量子力学框架下受Morse势影响的粒子的量子动力学。 通过采用引入反射对称性的Dunkl导数算符，我们构建了一个变形的Schrödinger方程，并利用Pekeris近似得到了精确的解析解。 由此得到的能量谱和波函数揭示了Dunkl参数如何改变有效势能和振动态。 该模型被应用于多个双原子分子，包括H$_2$、HCl和I$_2$，展示了对称性变形对能谱的影响。 我们还计算了热力学函数，包括配分函数、自由能、内能、熵和比热。 分析表明，Dunkl变形诱导了不同的热行为，并提供了一种可调的分子建模方法。 这些结果突显了Dunkl形式主义作为扩展常规量子模型以及探索分子物理和量子热力学中对称变形系统的潜在价值。 显示英文摘要

摘要： 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 Schr\"odinger 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 H$_2$, HCl, and 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.