摘要
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.
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.
作者
蔡俊
李敏
王群
CAI Jun;LI Min;WANG Qun(School of Physics and Electronic Engineering,Jiangsu Normal University,Xuzhou,Jiangsu 221116,China)
出处
《大学物理》
2021年第8期16-19,共4页
College Physics
基金
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)资助。
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
methods of mathematical physics
initial-value problem of three-dimensional wave equation
method of spherical means
spherically averaged function
