Through deliberated reasoning, the authors get very simple analytical expressions of the matrix elements of Hamiltonian operator, and obtain a convenient method of calculating the vibrational energy levels and wave functions for molecule systems.

• 经过详细的推导,证明了在分立位置表象中,哈密顿算符矩阵是对角占优、带状稀疏矩阵,矩阵元表达式具有特别简单的解析形式,计算时无需作积分运算,只要进行简单的代数运算,易于编程实现。