【摘要】 在量子动力学计算中,有时候为了规避奇点问题或者节省计算量,我们经常需要对哈密顿量进行变换.然而,在使用傅里叶基矢计算时,哈密顿量的变换形式容易导致哈密顿矩阵失去厄米性,进而有些情况下使数值计算变得不稳定.本文主要讨论构建具有厄米性的哈密顿算符的方法.以三原子分子为例,构建了键长一键角和Radau坐标下描述分子运动的各种形式的哈密顿量.基于这些哈密顿量,采用含时波包方法计算了OClO分子的吸收光谱,讨论了非厄米性矩阵对计算结果的影响.本文所得到的结论对基于基函数展开的量子动力学计算都是适用的.更多还原

【Abstract】 In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time.We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed.Otherwise,the Hamiltonian matrix becomes non-hermitian,which may lead to numerical problems.Methods for correctly constructing the Hamiltonian operators are discussed.Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian(J=0) in bond-bond angle and Radau coordinates are presented.For illustration,absorption spectra are calculated for the OCIO molecule using the time-dependent wavepacket method.Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors.The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.更多还原