基于Matlab软件的微振动理论及其应用  

The micro vibration theory and its application based on Matlab procedure

作　　者：李硕[1] 赵彤帆 宋海珍[1] 

机构地区：[1]南阳师范学院物理与电子工程学院,河南南阳473061 [2]河南省电教馆,河南郑州450004

出　　处：《南阳师范学院学报》2014年第6期56-60,共5页Journal of Nanyang Normal University

基　　金：河南省科技厅基础与前沿项目(132300410290);2012年河南省理论力学精品资源共享课程项目资助(教高【2012】1076号);河南省教师教育课程改革重点研究项目(2013-JSJYZD-053);南阳师范学院2013校级教研项目;南阳师范学院2013年STP项目(STP2013007)

摘　　要：介绍了Matlab软件在求解复杂理论物理问题中的应用.根据分析力学中的微振动理论,通过类比分析,得到一维单原子链系统经典方程的解和色散关系式.用算符代替力学量,简正坐标代替一般坐标,得到一维单原子链系统无交叉项的量子化方程和总能量表达式.实验结果分析得到双原子分子振动系统的能量和能级关系式.利用Matlab软件,求出微振动系统耦合方程组的解并实现解的可视化;展示一维单原子链振动系统色散关系的3-D图像;绘制双原子分子振动系统能级与能量的关系曲线.This paper introduces the application of Matlab procedure in solving complex problems in theoretical physics. According to the theory of micro vibration in analytical mechanics,by analogy,the relation of one-dimensional monatomic chain system classical equations to the dispersion is obtained. By using the operator instead of mechanical quantity,normal coordinate instead of general coordinates,quantized equation and the total energy expression are one-dimensional monatomic chain system without cross terms. Analysis of experimental results shows energy and energy relationship between the diatomic molecular vibration system. Using Matlab software,micro vibration system coupling equations are solved and the solution sualization is achieved,3-D images of onedimensional monatomic chain vibration dispersion relation is displayed and the relation curve of double atomic energy level and energy of molecular vibration system is plotted.

关 键 词：MATLAB软件 微振动 简正坐标 晶格振动 量子化 

分 类 号：O4-39[理学—物理]