数据驱动的精密双原子分子振动能谱研究进展

双原子分子系统因具有结构简单但能谱特征丰富的特点，成为量子力学各种理论模型的试金石和众多衍生应用学科的基本研究工具。其在精密测量、量子操控(如超冷分子)等前沿研究领域已经占据了重要的地位。本文回顾了精密双原子分子振动能谱近年来的研究进展，重点阐述了孙卫国课题组提出的变分代数法(VAM)，并通过分析PO分子的完全振动能谱，对该方法的优点和局限进行了详细讨论。最后，本文通过将该方法纳入更普遍的数据驱动的研究范式，探讨了VAM方法可能的发展方向，以期为获得更高精度的双原子分子振动能谱提供新的启示和思路。

Advances in the Study of Data-driven Precise Diatomic Molecular Vibration Energy Spectra

As for diatomic molecular system, the characteristics of simple structure and abundant energy spectrum makes it become the touchstone of various theoretical models of quantum mechanics and the basic research tools of many derived applications. It plays an important role in precision measurement, quantum manipulation (such as ultra-cold molecules) and other frontier research fields. This review mainly focuses on the progress in precise vibration energy spectrum of diatomic molecules in recent years. The variational algebraic method (VAM) proposed by Weiguo Sun's group is described in detail. The advantages and limitations of this method are discussed by analyzing the full vibration energy spectrum of PO molecule. Finally, by incorporating the method into a more general data-driven research paradigm, the probable development direction of the VAM method is presented in this paper, which may provide new inspiration and ideas for obtaining higher precision vibration energy spectra of diatomic molecule.