中文摘要：

对于极坐标系下的波动方程,首先通过引入合适的对偶变量将其化为Hamilton系统,并基于Bessel函数的性质证明了导出的Hamilton算子矩阵本征函数系的完备性定理,最后利用展开定理给出了Hamilton系统的解.

英文摘要：

The wave equation in the polar coordinates is firstly derived to the Hamiltonian sys- tem by choosing the appropriate dual variable. Moreover,a completeness theorem of the eigenfunc- tion system for the Harniltonian operator is proved by the properties of Bessel functions. Finally,the solution of the Hamiltonian system is given by the expansion theorem.