在球和柱坐标系下作用于矢量函数的拉普拉斯算子
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摘要
研究了在球和柱坐标系下作用于矢量函数的拉普拉斯算子的具体形式。基于球坐标和柱坐标系,从理论上对作用于矢量函数的拉普拉斯算子进行了分析和推导,发现它和作用于标量函数的拉普拉斯算子存在一定的关系,并用具体表达式进行了表示。
We have investigated the specific form of the Laplacian operator acting on the vector function in spherical and cylindrical coordinates. Based on the spherical and cylindrical coordinate systems,we analyzed and deduced the Laplacian operator acting on the vector function theoretically. It was found that it had some relation-ship with the Laplacian operator acting on the scalar function. Some specific expressions were given.
We have investigated the specific form of the Laplacian operator acting on the vector function in spherical and cylindrical coordinates. Based on the spherical and cylindrical coordinate systems,we analyzed and deduced the Laplacian operator acting on the vector function theoretically. It was found that it had some relation-ship with the Laplacian operator acting on the scalar function. Some specific expressions were given.
引文
[1]臧涛成,马春兰,潘涛.数学物理方法[M].北京:高等教育出版社,2014.
[2]谢处方,饶克谨.电磁场与电磁波[M].4版.北京:高等教育出版社,2006.
[3]郭硕鸿.电动力学[M].3版.北京:高等教育出版社,2014.
[4]李大潜,周忆.非线性波动方程[M].上海:上海科学技术出版社,2016.
[5]周世勋.量子力学教程[M].2版.北京:高等教育出版社,2009.
[6]张启仁.经典场论[M].北京:科学出版社,2004.
[7]JIN J M.Theory and Computation of Electromagnetic Fields[M].2th ed.New Jersey:John Wiley&Sons,Inc,2015.
[8]BOHREN C F,HUFFMAN D R.Absorption and Scattering of Light by Small Particles[M].New York:John Wiley&Sons,Inc,1983.
[9]HULST H C VAN DE.Light Scattering by Small Particles[M].New York:Dover Publications Inc,1957.
[10]ZHANG S J,JIN J M.Computation of Special Functions[M].New York:John Wiley&Sons,Inc,1996.
[11]MORSE P M,FESHBACH H.Methods of Theoretical Physics[M].New York:McGraw-Hill,1953.
[12]HARRINGTON R F.Time-Harmonic Electromagnetic Fields[M].New York:McGraw-Hill,2001.
[13]SUN J,HUANG Y,GAO L.Nonlocal composite media in calculations of the Casimir force[J].Phys Rev A,2014,89(1):012508.
[14]闫润卿,李英惠.微波技术基础[M].4版.北京:北京理工大学出版社,2011.
[15]方乐.拉普拉斯算子的直观物理意义[J].物理与工程,2018,28(1):54-56.
[16]金杰,张瑞峰.矢量拉普拉斯算符简析[J].电气电子教学学报,2018,40(1):102-104.
[17]ZHONG C P,ZHONG T D.Horizontal Laplace operator in real finsler vector bundles[J].Acta Mathematica Scientia,2008,28B(1):128-140.
[18]江俊勤.柱面坐标系和球面坐标系中的拉普拉斯算符[J].广东教育学院学报,2003,23(2):32-34.
[19]许超,董迎辉.随机障碍下动态基金保护的定价[J].苏州科技大学学报(自然科学版),2018,35(2):21-25.
[20]刘孔洁,董迎辉,朱海飞.超指数跳扩散模型下动态保护基金的定价[J].苏州科技学院学报(自然科学版),2016,33(1):41-44.
[2]谢处方,饶克谨.电磁场与电磁波[M].4版.北京:高等教育出版社,2006.
[3]郭硕鸿.电动力学[M].3版.北京:高等教育出版社,2014.
[4]李大潜,周忆.非线性波动方程[M].上海:上海科学技术出版社,2016.
[5]周世勋.量子力学教程[M].2版.北京:高等教育出版社,2009.
[6]张启仁.经典场论[M].北京:科学出版社,2004.
[7]JIN J M.Theory and Computation of Electromagnetic Fields[M].2th ed.New Jersey:John Wiley&Sons,Inc,2015.
[8]BOHREN C F,HUFFMAN D R.Absorption and Scattering of Light by Small Particles[M].New York:John Wiley&Sons,Inc,1983.
[9]HULST H C VAN DE.Light Scattering by Small Particles[M].New York:Dover Publications Inc,1957.
[10]ZHANG S J,JIN J M.Computation of Special Functions[M].New York:John Wiley&Sons,Inc,1996.
[11]MORSE P M,FESHBACH H.Methods of Theoretical Physics[M].New York:McGraw-Hill,1953.
[12]HARRINGTON R F.Time-Harmonic Electromagnetic Fields[M].New York:McGraw-Hill,2001.
[13]SUN J,HUANG Y,GAO L.Nonlocal composite media in calculations of the Casimir force[J].Phys Rev A,2014,89(1):012508.
[14]闫润卿,李英惠.微波技术基础[M].4版.北京:北京理工大学出版社,2011.
[15]方乐.拉普拉斯算子的直观物理意义[J].物理与工程,2018,28(1):54-56.
[16]金杰,张瑞峰.矢量拉普拉斯算符简析[J].电气电子教学学报,2018,40(1):102-104.
[17]ZHONG C P,ZHONG T D.Horizontal Laplace operator in real finsler vector bundles[J].Acta Mathematica Scientia,2008,28B(1):128-140.
[18]江俊勤.柱面坐标系和球面坐标系中的拉普拉斯算符[J].广东教育学院学报,2003,23(2):32-34.
[19]许超,董迎辉.随机障碍下动态基金保护的定价[J].苏州科技大学学报(自然科学版),2018,35(2):21-25.
[20]刘孔洁,董迎辉,朱海飞.超指数跳扩散模型下动态保护基金的定价[J].苏州科技学院学报(自然科学版),2016,33(1):41-44.