推廣的赫姆霍茲定理及其在電磁理論中的應(yīng)用
EXTENDED HELMHOLTZ THEOREM AND ITS APPLICATION IN ELECTROMAGNETIC THEORY
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摘要: 本文證明了在直角、畫柱和球坐標(biāo)系的規(guī)則邊界的系統(tǒng)內(nèi),一個(gè)任意的矢量一定可以分解為無(wú)旋場(chǎng)、橫電模場(chǎng)和橫磁模場(chǎng)三個(gè)相互正交的分量,每一個(gè)分量都可用一個(gè)標(biāo)量函數(shù)來(lái)描述。并在此基礎(chǔ)上證明了這些系統(tǒng)內(nèi)的{L、M和N}矢量波函數(shù)系的完備性。由此說(shuō)明了一個(gè)矢量函數(shù)空間不僅可以通過(guò)它在歐氏空間中的射影分解為三個(gè)不相交的子空間,同樣可以通過(guò)它在矢量波函數(shù)系上的射影分解為三個(gè)不相交的子空間。
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關(guān)鍵詞:
- 電磁理論; 赫姆霍茲定理; 無(wú)旋場(chǎng)
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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