Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Does the Creation Operator a + Possess Eignvectors?

Fan Hong-Yi, Zu-wei Liu, Ruan Tu-Nan

Published Mar 1, 1984• 33 citations
Publisher

Abstract

It is pointed out that the assertion that the eigenfunction of the creation operator a + is identically zero is not rigorous. On the contrary, the eigenfunction of a + may be discussed by using the contour integral representation of δ function, the property of which and the relation with the eigenstate of the annihilation operator are discussed. Its applications, especially the application in thoroughly studying the inverse operator's properties, are presented. It is shown that the phase operator can also be represented by the inverse operator.

DOI
10.1088/0253-6102/3/2/175

Related papers

THE EIGENVECTORS OF q-DEFORMED CREATION OPERATOR $a_q^+$ AND THEIR PROPERTIES

Guo-xin Ju, Jin-He Tao, Zixin Liu +1 more

The eigenvectors of q-deformed creation operator [Formula: see text] are discussed for q being real or a root of unity by using the contour integral representation of δ function. The properties for the eigenvectors are also discussed. In the case of qp = 1, the eigenvectors may be normalizable.

Modern Physics Letters A•Mar 14, 1995•0 citations

On q -Defomed Creation Operator a †

Yang Yaping, Chunfeng Zhao, Zurong Yu

In this paper, we construct the eigenstate of q -deformed creation operator a † by using the contour integral representation of δ function. Some of its properties are presented.

Communications in Theoretical Physics•Sep 15, 1997•0 citations

Left-hand and right-hand inverse operators of quantum operators and its mathematical property

Shimin Xu, Yunhai Zhang, Xing-Lei Xu +1 more

The right-hand inverse operator of the annihilation operators and the left-hand inverse operator of the creation operator are given by using the contour integration. Furthermore, the corresponding relation between the right-hand inverse or left-hand inverse operator derived and the column elementary transformation or row transformation of a matrix is investigated.

Acta Physica Sinica•Jan 1, 2010•1 citation

Eigenkets of the q-deformed creation operator

Ye‐Jun Xu, Jun Song, Hong-Yi Fan +1 more

By using the contour integral representation of δ-function and the technique of integration within an ordered product of operators, we point out that the q-deformed creation operator possesses the eigenkets. A set of new completeness and orthogonality relations composed of the kets and bras which are not mutually Hermitian conjugates are derived. Application of the completeness relation in constructing the generalized P-representation of density operator is demonstrated.

Journal of Mathematical Physics•Sep 1, 2010•2 citations

δ-Function Operator Formulas of Photon Creation and Annihilation Operators

Fan Hong‐Yi, Fan Yue

Using the technique of integration within an ordered product of operators we derive some δ-function operator formulas of photon creation and annihilation operators. Applications of these new formulas in simplifying some Louisell's operator theorems and in discussing the eigenket of creation operator are presented.

Communications in Theoretical Physics•Mar 15, 1998•0 citations

Inverse operators in Fock space studied via a coherent-state approach

Fan Hong‐Yi

The Fock representation of the inverse of harmonic-oscillator creation and annihilation operators [see, e.g., C. L. Mehta, Anil K. Roy, and G. M. Saxena, Phys. Rev. A 46, 1565 (1992)] are naturally derived via a coherent-state approach. The completeness relation of Fock space is reexpressed by the inverse operators. Applications of the inverse operators in studying the phase operators and in normally ordering some operators are given.

Physical Review A•May 1, 1993•29 citations
It is pointed out that the assertion that the eigenfunction of the creation operator a + is identically zero is not rigorous. On the contrary, the eigenfunction of a + may be discussed by using the contour integral representation of δ function, the property of which and the relation with the eigenstate of the annihilation operator are discussed. Its applications, especially the application in thoroughly studying the inverse operator's properties, are presented. It is shown that the phase operator can also be represented by the inverse operator.
THE EIGENVECTORS OF q-DEFORMED CREATION OPERATOR aq+a_q^+aq+​ AND THEIR PROPERTIES