波动方程Hamilton算子本征值问题的Green矩阵与本征函数系的完备性

On Green Matrix of the Eigenvalue Problem and Completeness of the Eigenfunction Systems for a Hamiltonian Operator Derived from the Wave Equations

从积分方程角度出发,研究了波动方程导出的无穷维Hamilton算子的本征函数系的完备性问题.首先计算了Hamilton算子本征值问题导出的非齐次边值问题的Green函数矩阵,其次利用Green函数法证明了无穷维Hamilton算子本征函数系的完备性.文中的方法对某些辛弹性力学模型的研究具有一定借鉴意义.

Completeness problem of eigenfunction systems of an infinite-dimensional Hamiltoni- an operators derived from the wave equations is considered from the perspective of integral equa- tions. Firstly,the matrix of Green functions is obtained for the nonhomogeneous eigenvalue equa- tions of the Hamiltonian operator. Secondly,the completeness of the eigenfunction systems is prov- en by the method of Green functions. The method used can be as a reference for the study of some symplectic elasticity models.