MATLAB在量子力学学习中的应用  

Application of MATLAB to the study of quantum mechanics

作　　者：周群益 莫云飞 周丽丽[3] 侯兆阳 ZHOU Qun-yi;MO Yun-fei;ZHOU Li-li;HOU Zhao-yang(Guangzhou Institute of Science and Technology,Guangzhou,Guangdong 510540,China;School of Electronic Information and Electrical Engineering,Changsha University,Changsha,Hunan 410022,China;Department of Information Engineering,Gannan Medical University,Ganzhou,Jiangxi 341000,China;School of Science,Chang’an University,Xi’an,Shaanxi 710064,China)

机构地区：[1]广州理工学院,广东广州510540 [2]长沙学院电子信息与电气工程学院,湖南长沙410022 [3]赣南医学院信[JZ]息工程学院,江西赣州341000 [4]长安大学理学院应用物理系,陕西西安710064

出　　处：《大学物理》2021年第6期19-25,共7页College Physics

基　　金：广东省高校科研特色创新项目(2020KTSCX209);国家自然科学基金(12004053)资助。

摘　　要：指出了《工科量子力学学习中的常用数学工具》一文中的一些差错,列出了正确的公式.量子力学的公式比较多,解决计算问题的最佳工具应该是MATLAB.用MATLAB说明了极限的算法,积分的算法,常微分方程的解法,狄拉克函数的表示和算法,伽玛函数和贝塔函数的用法,特殊函数的算法.以一维线性谐振子为例,说明了MATLAB在量子力学中的应用.MATLAB还能计算氢原子中电子出现的概率密度,并用图形表现出来.This paper points out some errors in the article of“Commonly using mathematical tools in the course of quantum mechanics”and lists the correct formula.There are many formulas in quantum mechanics,while the optimal tool for solving calculation problems should be MATLAB.In this paper,with help of MATLAB,we have illustrated the algorithm of limit,the algorithm of integration,the solution of ordinary differential equations,the representation and algorithm of Dirac function,the usage of gamma function and beta function,and the algorithm of special functions.One-dimensional linear harmonic oscillator has been taken as an example,which can reflect the application of MATLAB in quantum mechanics.MATLAB can also calculate and show the graphics about the probability density of the emergence of electrons in hydrogen atoms.

关 键 词：量子力学 数学工具 MATLAB 

分 类 号：O4-1[理学—物理]