用算子代数计算氨的反转能级
Ammonia Inversion Energy Levels using Operator Algebra
摘要：
氨分子的反转势近似为四次函数。因此，哈密顿量只包含p和x的偶数次幂，并建议用梯形算符a和a^+表示。出现在运营商的频率变量ω被引入作为一个自由参数，其值被确定，如优化协议与实验结果。使用已知的氨分子的结构参数，计算的哈密顿矩阵的10 × 10截断的本征值。两个最低本征值之间的分裂对应于氨脉泽频率24.87 GHz，该值通过适当选择Ω来再现。
英文摘要：
The inversion potential for the ammonia molecule is approximated by a quartic function. The Hamiltonian thereby contains only even powers of p and x and a representation in terms of ladder operators a and a^+ is suggested. The frequency variable omega occurring in the operators is introduced as a free parameter, with its value to be determined such as to optimize agreement with experimental results. Using known structural parameters of the ammonia molecule, the eigenvalues for a 10 by 10 truncation of the Hamiltonian matrix are computed. The splitting between the two lowest eigenvalues corresponds to the ammonia maser frequency, 24.87 GHz, this value being reproduced by the appropriate choice of omega.
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