李代数方法在分子振动光谱研究中的应用

The application of Lie algebra method in the research of molecular vibrational spectroscopy

通过对动力学对称性的介绍,引出构造分子体系Hamiltonian的方法,并介绍李代数方法处理分子"振动-振动耦合"、"振动-转动耦合"Hamiltonian的一般步骤.还以HCO分子体系为例,说明如何选取特定的群链来构造Hamiltonian,并论证了对于该体系群链的唯一性.最后还对一些李代数方法在分子光谱中的其他应用(例如局域模,多原子分子的振转光谱研究)作了初步的介绍,并对于这一方法的不足和局限性做了论述.

Through the introduction of dynamical symmetry, the method of construct the Hamiltonian of the molecule is derived and the general method of dealing with ＂vibration-vibration coupling＂ and ＂vibration-rotation coupling＂ molecular spectroscopy are deduced. An example （HCO molecule） is induced to elucidate this method by choosing a certain group chain to construct Hamiltonian of this molecular system and illustrating that the group chain is unique. It also makes a principal introduction of some other applications of Lie algebra method in the molecular spectroscopy （e. g. local-mode, the spectroscopy＇of multi-atomic molecule） and elucidates some question of this method in the last of this paper.