摘要
本文讨论了谐振腔中亥姆霍兹定理的合理形式,即谐振腔内的电场怎样分解为相互正交的电旋量场和电无旋场的形式。并由此证明:电无旋场可在L类矢量波函数上展开成一收敛的级数,而旋量场可在M和N类矢量波函数上层开成一收敛的级数。这样也就证明了L,M和N类矢量波函数,对谐振腔内的电场组成了一个完备的正交基。
The rational form of Helmholtz theorem in resonant cavity is discussed. On the basis of the theorem, it is proved that the electric irrotational field can be expanded into a convergent series on L vector wave function, and that the electric rotational field also can be expanded into a convergent series on M and N vector wave functions. So it is proved that L,M and N vector wave functions consist of a complete orthogonal basis for electric field in resonant cavity.
基金
国家自然科学基金
关键词
谐振腔
亥姆霍磁定理
电磁场
函数
Operator theory of electromagnetic field
Helmholtz theorem
Resonant ca- vity
Expansions of eigenfunctions of electromagnetic field
