【摘要】 证明了广义的亥姆赫兹定理——电磁场在矢量波函数空间的完全射影定理。在这一定理中每一个任意的电磁矢量函数都可以在矢量波函数空间中被唯一地分离成三个独立的分量，每一个分量都可以用一个标量函数来表示。这种电磁矢量在矢量波函数空间的完全射影定理不论对于电磁场的解析理论还是数值方法都有非常重要的应用价值。更多还原

【Abstract】 The widely used Helmholtz theorem separates an arbitrary function into two parts: one is an irrotational component which can be expressed by a scalar function and the other is a rotational part which can only be expressed by another vector function. So it is considered as incomplete projection of a vector function. In this paper, the generalized theorem is proved. In this theorem an arbitrary vector function is separated into three parts each one can be expressed as a scalar function. It is the complete projection for a vector function in vector wave function space. And the widely applications of this theorem for electromagnetic field theory are discussed as well, such as for solving eigenproblems of resonant cavity by numerical method or Dyadic Green’s function.更多还原