坐标本征矢的谐振子表示及完备性  

A demonstration of completeness of coordinate eigenvectors

作　　者：李体俊[1] 

机构地区：[1]菏泽学院物理系

出　　处：《大学物理》2009年第1期25-27,共3页College Physics

摘　　要：借助粒子数算符的本征矢及其完备性,得到了用实数x、产生算符及粒子基态表示的矢量|x〉.以此为起点,证明了矢量|x〉是坐标算符的本征矢,坐标投影算符的积分是单位算符,坐标本征矢是正交归一的.因此,坐标本征矢集{|x〉}具有正交归一性和完备性.A vector ｜x〉 expressed by the real number x, the creation operator and the ground state of particle number operator is obtained in terms of the eigenvectors and the completeness relation of particle number operator. It is proved that the vector ｜x〉 is the eigenvector of coordinate operator; the integral over coordinate projective operators is equal to the identity operator; and the eigenvectors of coordinate operator are orthogonal. Hence all eigenvectors { ｜x〉 } form a complete and orthogonal set of basic vectors in an infinite-dimensional vector space.

关 键 词：粒子数算符的本征矢 坐标算符的本征矢 投影算符的积分 坐标本征矢的完备性 

分 类 号：O413.1[理学—理论物理]