D维空间Cs_2分子X^1Σ_g^+态精确解析解

Exact analytical solution to X^1Σ_g^+ state of Cs_2 molecule in D spatial dimensions

使用完全量子化规则法计算了D维空间中具有任意转动量子数Morse势的Schrdinger方程,得到了Cs_2分子X^1Σ_g^+态旋转-振动能谱,讨论了能谱与维度D和振动量子数之间的关系.结果表明:(1)具有不同转动量子数和振动量子数的能谱随维度D的增大而趋于相同;(2)高维Cs_2分子X^1Σ_g^+态的振动能特性与三维相似.

The Schrodinger equation including Morse potential with arbitrary rotational quantum number in D spatial dimensions was investigated using the proper quantization rule approach. The rotation -vibrational energies for X^1Σg^＋state of Cs2 molecule were obtained. We discussed the relations of the energy spectra with spatial dimension D and vibrational quantum number. The results show that, （1） the rotation -vibrational energies for X^1Σg^＋ state of Cs2 molecule converge as D increases in the presence of a fixed vibrational quantum number and various rotational quantum numbers, and （2） the behavior of the vibrational energies in higher dimensions remains similar to that of the three - dimensional system.