量子力学中厄米算符本征矢完备性的限制和界定

摘要

From the start vector Hermitian operators to fully set definition. In the complete set of the system (referred to as the collection system) as the standard, through discussion and collections within the collection system outside the system Hermitian operators eigenvectors completeness limits to arrive at a Hermitian operators own complete system of general proof. Then come completeness should be based on the complete set of comprehensive, strictly speaking, when talking about a completeness of eigen vectors operator, whose standpoint is very special, that we should default the operator itself is a complete collection or, in saying this operator Eigenvector space when complete set of its range is limited to within the operator domain and range where the Hilbert space.%从厄米算符矢开始，以完全集合定义出发，以完全集合体系（简称集合体系）为标准。通过讨论集合体系内厄米算符本征矢量完备性限制，从而得出了厄米算符自身体系完备性的一般证明。进而得出完备性应该在是完全集合基础上的完备，严格说起来，谈论一个算符本征矢的完备性时，其立足点是非常特殊的，这时候应该默认这个算符本身就是一个完全集合，或者在说这个算符本征矢为完备组时其空间范围限定为在这个算符定义域和值域所在的希尔伯特空间之内。