球谐基函数数学实现的一种群方法

Group Method for Realization of Spherical Basis Functions

根据球对称物体的对称特点构造三维转动群(SO3),利用群论中的完备算符集理论,通过群变换方法求得该群的分类基,该分类基就是传统意义的球谐函数.研究表明利用群变换方法完全可以实现复杂对称结构边界的基函数,为矩量法求解复杂边界电磁散射问题提供了一个新途径.

Based on the geometric feature of spherically symmetric structures, a 3D rotation group, SO3, was constructed. By applying the group theory of complete set of calculation operators, the classified basis functions of this group, i.e. the spherical functions, were obtained through group transformations, being identical with ones obtained using the traditional variable separation method. The result shows that the basis functions of a spherically symmetric structure can be obtained completely through group transformations, and as a result, the research provide a new way to solve electromagnetic scattering problems with complicated boundaries by using the moment method.