推广的赫姆霍兹定理及其在电磁理论中的应用
EXTENDED HELMHOLTZ THEOREM AND ITS APPLICATION IN ELECTROMAGNETIC THEORY
-
摘要: 本文证明了在直角、画柱和球坐标系的规则边界的系统内,一个任意的矢量一定可以分解为无旋场、横电模场和横磁模场三个相互正交的分量,每一个分量都可用一个标量函数来描述。并在此基础上证明了这些系统内的{L、M和N}矢量波函数系的完备性。由此说明了一个矢量函数空间不仅可以通过它在欧氏空间中的射影分解为三个不相交的子空间,同样可以通过它在矢量波函数系上的射影分解为三个不相交的子空间。
-
关键词:
- 电磁理论; 赫姆霍兹定理; 无旋场
Abstract: It is proved that in a regular boundary system of rectangular, cylindrical or spherical coordinate, an arbrtrary Vector function can be separated into three orthogonal parts: TE mode field, TM mode field and irro tational field. Each of these components can be determined fully by a scalas function. On the basis of this theorem, the compltenesa of vector wave function system {L, M, and N} is proved, also. Thus it is explained that a vector furction space can be proiected into three uncrossed subspaces not only in Euclidean space but also in the subspace of vector wave function space. -
P. M. Morse, F. Feshback, Math. of Theoretical Phys., Pt. I, McGraw-Hill Book Company,New York.(1953).[2]宋文森,微波,1986年,第3期,第23-28页.[3]林为干,微波理论和技术,科学出版社,(1979), p.671.[4]Wang Jianying, Song Wenmiao, Helmholtz's Theorem and Expansions of Eigentunctions of EM Field in Resonant Cavity, APMC88, The Second Asia-Pacitic Microwave Conference, Beijing,(1988), p. 85.[5]J. D.杰克逊著,朱培予译,经典电动力学,上册,人民教育出版社,(1980),p.244.[6]O. L. Brill, H. Grodman, Am. J. Phys., 35(1967), 832.[7]宋文森,电子科学学刊,8(1986)3, 188-195.[8]K. Kurokawa, IRE Trans. on MTT, MTT-6 (1958), 178-187.[9]龚书喜,电磁理论中广义本征函数展开间题,西安交通大学博士论文,1987年.[10]宋文森,微波学报,1989年,第3期,第21-28页.[11]R. E. Collin, Rodio Science, 21(1986), 883-890.[12]宋文森,王建英,电子科学学刊, 11(1989)5, 518-527. -
计量
- 文章访问数: 2327
- HTML全文浏览量: 124
- PDF下载量: 629
- 被引次数: 0
下载:
