电磁理论中算符的一些性质

在本文中,把在不均匀各向异性介质中的麦克斯韦方程看作算符,它定义在一个有界区域,可以被理解为微波技术中的谐振腔。但在这腔中充填着铁氧体,等离子体或其他各向异性介质,这些介质在应用中日益重要。文中证明了在某些μ、ε和边界条件下,算符成为对称。而对称性和自伴性在本征函数展开中带来很多方便;此外我们推导了本征振动的正变性和互易定理。如果不满足对称性,引入伴谐振腔的概念,所谓伴谐振腔在几何形状上和原来的腔相同,但ε、μ和边界条件不一样。它和自伴谐振腔在正交性和互易定理上有某些相似之处。

SOME PROPERTIES OF OPERATOR IN ELECTROMAGNETIC THEORY

In this paper we studied the Maxwell's equations in imhomogeneous and anisotropic media as an operator. It is defined in a bounded region, which can be comprehended as a resonant cavity in micro-wave technique. But these cavities are filled with ferrite, plasma or other gyrotropic medium, all these new media become more and more important in practice. We proved that under some concrete conditions imposed on μ, ε and restrictions on the boundary value, the operator of Maxwell's equations becomes a symmetric one. The symmetry and self-adjoint property give much convenience in eigenfunction expansion problems. Besides, we derived the orthogonality of characteristic oscillation and reciprocity theorem in general.If it does not satisfy the conditions of symmetry, we introduced the concept of adjoint-cavity. The so-called adjoint cavity coincides with the primary cavity in geometrical shape, but both μ, ε and boundry conditions do not coincide. It has some properties similiar with self-adjoint cavity in orthogonality and reciprocity theorem.