本文系统地表述了格林函数法的基本思想,证明格林函数倒易关系只适用于自伴算符,格林函数的齐次边界条件也来自于微分算符的自伴性,非自伴算符的微分方程不能直接应用格林积分公式.文章还描述了由格林函数带来的微扰展开法,展示了其与物理学中广泛应用的费曼图技术的关系,以便学生在学习高等物理时理解其内在逻辑.

The paper systemically describes the fundamental principle of the Green^,s function method. It demonstrates that the reversal relation holds only for the case of self-adjoint operator. The homogeneous boundary condition of the Green^,s function also comes from the self-adjointness of the differential operator while the Green integral formula does not directly apply to the non-self-adjoint operator. The paper also addresses perturbation expansion method induced by the Green^,s function, shows its relation to the popular Feynman diagram technique in physical science so as to help the student understanding the internal logics when learning advanced physics.