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
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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。
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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. -
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