厄米算符本征函数完备性的一般证明

The general proof of completeness of eigenfunction of Hermitian operators

从一组完备的本征函数开始,以表象原理为前提,建立一个唯象的公式,利用反证法证明了力学量算符的完备性,即这一组完备的本征函数可以投影到力学量算符的本征函数空间中.从而给出了力学量算符本征函数完备性的一般证明.

Starting from a set of completed eigenfunctions, we build a phenomenological formula under the rep-resentation principle, and then the completeness of eigenfunction of the Hermitian operators is proved by reduction to absurdity. This set of completed eigenfunctions of mechanical quantities can be projected onto the eigenfunctions of operator space, which gives the general proof of completeness of eigenfunctions of operators.