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Acta Physica Sinica

Expressions of coordinate eigen vectors and their integration over non-symmetric coordinate projective operators

LI Ti-jun, 菏泽学院物理系,菏泽 274015

Published Jan 1, 2008• 1 citation
Publisher

Abstract

The coordinate state vector 〈f(x)| is expressed with 〈x| in virtue of particle number states and the eigen equations of coordinate operator functions,accordingly we can convert non-symmetric projective operators into symmetric,the integrations over non-symmetric projective operators are obtained by the completeness relation of coordinate eigenstates.

DOI
10.7498/aps.57.3969

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The coordinate state vector 〈f(x)| is expressed with 〈x| in virtue of particle number states and the eigen equations of coordinate operator functions,accordingly we can convert non-symmetric projective operators into symmetric,the integrations over non-symmetric projective operators are obtained by the completeness relation of coordinate eigenstates.
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 op- erators is equal to the identity operator;and the eigenvectors of coordinate operator are orthogonal.Hence all eigen- vectors {|x〉} form a complete and orthogonal set of basic vectors in an infinite-dimensional vector space.