分立位置表象中双原子分子振动能级的计算

Calculation of the vibrational energy-level for the diatomic molecules in the discrete position presentation

用离散的位置基矢作为连续位置基矢的近似 ,构建分立位置表象。在分立位置表象中 ,哈密顿算符矩阵具有对角占优、带状稀疏的特点 ,矩阵元不用做积分运算 ,具有特别简单的解析表达式。分别对双原子分子在Morse势、Murrell Sorbie势和双阱势中运动情形 ,进行了数值计算。结果表明 ,在分立位置表象中计算双原子分子振动能级 ,方法简便 ,稳定性好 。

By using the discrete position base-vectors approximating for the continuous position base-vector, the discrete position presentation is constructed. In this presentation, Authors discuss the method of discreting Hamiltonian operator and obtain the matrix form of the Schr*idinger equation. Based Fourier transforms, the expression of kinetic energy operator is derived from the momentum presentation and the truncation error from the finite difference method is avoided. As examples, for the diatomic molecules in Morse, Murrell-Sobie and double-well potential, the vibrational energy level are calculated respectively. The result shows that the calculation in the discrete position presentation has characters of the simplicity, high stability and accuracy.