引用本文格式: 郑兴荣,杨伟,张馨丹,杜晨敏,李小龙,唐歡. 基于MATLAB对球谐函数及其原子轨道的可视化研究 [J]. 四川大学学报: 自然科学版, 2020, 57: .
 
基于MATLAB对球谐函数及其原子轨道的可视化研究
Visualization research of the spherical harmonic function and atomic orbital based on MATLAB software
摘要点击 193  全文点击 38  投稿时间:2020-01-22  修订日期:2020-03-18
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DOI编号   
中文关键词   球谐函数  原子轨道  连带勒让德方程  可视化研究  角动量算符  分离变量法  数值仿真
英文关键词   Spherical harmonic function  Atomic orbitals  Associated Legendre equation  Visualization research  Angular momentum operators  Separation variable method  Simulation
基金项目   高校基金
作者单位E-mail
郑兴荣 陇东学院电气工程学院物理系 zhengxingrong2006@163.com 
杨伟 陇东学院电气工程学院物理系  
张馨丹 陇东学院电气工程学院物理系  
杜晨敏 陇东学院电气工程学院物理系  
李小龙 陇东学院电气工程学院物理系  
唐歡 陇东学院电气工程学院物理系  
Author NameAffiliationE-mail
ZHENG Xing-Rong Department of Physics, College of Electrical Engineering, Longdong University zhengxingrong2006@163.com 
YANG Wei Department of Physics, College of Electrical Engineering, Longdong University  
ZHANG Xin-Dan Department of Physics, College of Electrical Engineering, Longdong University  
DU Cheng-Min Department of Physics, College of Electrical Engineering, Longdong University  
LI Xiao-Long Department of Physics, College of Electrical Engineering, Longdong University  
TANG Huan Department of Physics, College of Electrical Engineering, Longdong University  
中文摘要
    球谐函数是拉普拉斯方程的球坐标系形式解的角度部分,在经典场论、量子力学等领域广泛应用.基于量子力学中的角动量算符和连带勒让德方程,设定广义函数的条件下,利用分离变量法推导出球谐函数的一般方程式,进而解出n、l分别为0,1,2,3,4,5时的球谐函数.另外,根据球坐标的自变量定义域,设定自变量θ、φ的条件下,得到了不同状态的球谐函数及其原子轨道,并对其进行了可视化研究.最后,利用 MATLAB软件对不同的n、l所对应的球谐函数和原子轨道进行仿真模拟,得到了简明扼要、直观清晰的可视化结果.这种可视化的研究思路为研究球谐函数及其原子轨道的其他特性提供了一条便利的途径.
英文摘要
    The spherical harmonic function is the angular part of the form solution of the spherical coordinate system of the Laplace equation. It is widely used in classical field theory, quantum mechanics and other fields. Based on the angular momentum operator and associated Legendre equation in quantum mechanics, the general equation of spheric harmonic function is deduced using the separation variable method under the generalized function condition, and then the spherical harmonic function is obtained when n and l are 0, 1, 2, 3, 4 and 5, respectively. According to the independent variable domain of spherical coordinate, under the independent variables θ, φ condition, spheric harmonic function and its atomic orbitals at different states are studied, and the visualization research is made. Finally, using MATLAB software, we simulate spheric harmonic function and its atomic orbitals at different n, l, then obtain concise, readable and clear visualization results. The visualization study provides a feasible way to investigate other characteristics for spheric harmonic function and its atomic orbitals.

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