球面平均值函数及其微分方程的推导

教学讨论

球面平均值函数及其微分方程的推导

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蔡俊( 1981—) ，男，江苏泰州人，江苏师范大学物理与电子工程学院讲师，博士，主要从事理论物理教学与研究工作.

收稿日期: 2021-01-10

修回日期: 2021-03-17

网络出版日期: 2021-08-24

基金资助

教育部高等学校物理学类专业教学指导委员会数学物理方法课程教学研究项目( jzw- 15-sl- 05) ; 国家自然科学基金( 11447015)

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Spherically averaging function and deduction of its differential equation

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School of Physics and Electronic Engineering，Jiangsu Normal University，Xuzhou，Jiangsu 221116，China

Received date: 2021-01-10

Revised date: 2021-03-17

Online published: 2021-08-24

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三维波动方程初值问题是数学物理方法课程的重要教学内容. 本文讨论球面平均法求解该问题时，球面平均值的定义及其满足的偏微分方程的建立过程.

在教材常见推导的基础上，本文提出了球面平均值方程一种更简洁的推导方法. 本文的讨论有利于澄清球面平均值函数的含义，为球面平均法以及球坐标系下数学物理方程的教学提供参考.

关键词： 数学物理方法; 三维波动初值问题; 球面平均法; 球面平均值

蔡俊, 李敏, 王群 . 球面平均值函数及其微分方程的推导[J]. 大学物理, 2021 , 40(8) : 16 . DOI: 10.16854 / j.cnki.1000-0712.210016

The initial- value problem of the wave equation in the three-dimensional case

is a very important content in the course of methods of mathematical physics. In this paper，we

discuss the definition of the spherically

averaging function and how to build up the partial differential equation satisfied when we use the

method of spherical means to solve this problem. A more concise procedure to deduce the

equation of spherically averaging function is provided based on the analysis of the

deduction appeared in the textbooks. Our discussion will clarify the basic meaning of the

spherically averaged function and is benefit to the teaching and studying of the method of

spherical means and other solutions to the equations of mathematical physics in three-dimensional

spherical coordinates.

Key words： methods of mathematical physics; initial - value problem of three-dimensional wave equation; method of spherical means; spherically averaged function

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