MATLAB计算分子振动本征值和本征函数

The calculation of molecular vibrational eigenvalues and eigenfunctions via MATLAB

分子动力学和分子光谱等的研究中,常常需要计算分子的振动本征值和振动本征函数。采用传统计算语言编程实现,往往繁琐而困难。MATLAB语言以矩阵为基本元素,自带的库函数可以高效便捷地解决计算其中涉及的许多数学问题。本文采用MATLAB语言计算了Morse势和双井(double well)势的振动本征值和振动本征函数。结果表明,MATLAB语言用于分子振动本征值和本征函数的计算,是一种简洁、高效的运算工具。所编制的程序具有普适性,只需对势能函数进行简单修改即可用于真实双原子分子的振动计算。

The molecular vibrational eigenvalues and eigenfunctions are very important in the study of molecular dynamics and molecular spectroscopy.It is often tedious and difficult by using traditional programming language such as Fortran or C to solve these problems.As a fourth-generation programming language,MATLAB allows matrix manipulations and provides many built-in functions.We calculated the vibrational eigenvalues and eigenfunctions of Morse potential and double well potential with MATLAB Language.The program is universal. User only need to modify the potential function in the calculation of diatomic molecular vibration.