EXTENDED HELMHOLTZ THEOREM AND ITS APPLICATION IN ELECTROMAGNETIC THEORY

It is proved that in a regular boundary system of rectangular,cylindrical or sphericalcoordinate,an arbitrary vector function can be separated into three orthogonal parameters:TEmodel field,TM model field and irrotational field.Each of these components can be determinedfully by a scalar function.On the basis of this theorem,the completeness of vector wave functionsystem{L,M,and N}is proved also.Thus it is explained that a vector function space can beprojected into three uncrossed subspaces not only in Euclidean space but also in the subspace ofvector wave function space.

Extended helmholtz theorem and its application in electromagnetic theory

It is proved that in a regular boundary system of rectangular,cylindrical or spherical coordinate,an arbitrary vector function can be separated into three orthogonal parameters:TE model field,TM model field and irrotational field.Each of these components can be determined fully by a scalar function.On the basis of this theorem,the completeness of vector wave function system{L,M,and N}is proved also.Thus it is explained that a vector function space can be projected into three uncrossed subspaces not only in Euclidean space but also in the subspace of vector wave function space.