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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。
In the research of molecular dynamics and molecular spectroscopy, it is often necessary to calculate the eigenvalues of vibration and eigenfunction of vibration. The traditional calculation of language programming, often cumbersome and difficult. MATLAB language to the matrix as the basic element, the library function comes with efficient and easy to solve the calculation of many of the mathematical problems involved. In this paper, the vibration eigenvalues and vibration eigenfunctions of Morse potential and double well potential are calculated by MATLAB language. The results show that the MATLAB language is used to calculate the eigenvalue and eigenfunction of molecular vibration, which is a simple and efficient computing tool. The program is universal and can be used for the vibration calculation of real diatomic molecules with a simple modification of the potential energy function.