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

Acta Sinica Quantum Optica

New Approach for Introducing Wigner Function,Weyl Correspondence and the Coherent State Representation of Wigner Operator

Fan Hong‐Yi

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

By using the normal ordering form of the coordinate,momentum completeness,we directly and concisely introduce the Wigner operator and then illustrate its relation with the Weyl correspondence.The coherent state representation of the Wigner operator is also neatly derived.

Related papers

New Formulation of Weyl Quantization Scheme in Coherent State Representation

Tang-Kun Liu, Hong-Yi Fan

By virtue of the technique of integration within an ordered product of operators we present a new formulation of the Weyl quantization scheme in the coherent state representation, which not only brings convenience for calculating the Weyl correspondence of normally ordered operators, but also directly leads us to find both the coherent state representation and the Weyl ordering representation of the Wigner operator.

Communications in Theoretical Physics•Jan 1, 2011•1 citation

Coherent State Formulation of the Weyl Correspondence and the Wigner Function

Fan Hong-Yi, Ruan Tu-Nan

We point out that there is a close connection between the Weyl correspondence and coherent state correspondence. By virtue of differential and integral method within normal ordered products we demonstrate that the essence of the Weyl correspondence is just coherent state correspondence in both boson and fermion cases. Furthermore, coherent state form and explicit operator form for the Wigner function are given. With these forms we can derive some important operator formulas from the Weyl correspondence. The Wigner function's zero-point value is also discussed.

Communications in Theoretical Physics•Nov 1, 1983•48 citations

Recapitulating Quantum Phase Space Representation by Virtue of Normally Ordered Gaussian Form of Wigner Operator

Fan Hong‐Yi, Xing-Lei Xu, Hongqi Li

Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector |q⟩ λ,ν of linear combination of the coordinate and momentum operator, (λQ + νP), where λ, ν are real numbers, and |q⟩ λν is complete, then the projector |q⟩ λν ⟨q| must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.

Communications in Theoretical Physics•Feb 1, 2010•1 citation

Some Applications of the Coherent State Formulation of the Wigner Operator

Fan Hong‐Yi, Ruan Tu-Nan

On the basis of the preceding paper we present some new applications of both the normal product form and the coherent state form of the Wigner operator, which involve deriving some new quantum operator formulas, giving the coherent state generalization of the Moyal theorem, evaluating some quantum operators which correspond to the given classical functions in the weyl manner and vice versa. Were it not for the Wigner operator's coherent state formulation given by us the above-mentioned calculations would be hard to perform.

Communications in Theoretical Physics•May 1, 1984•44 citations

SOME APPLICATIONS OF COHERENT STATE FORMULATION OF THE WIGNER OPERATOR

Heng Fan

In this paper both the normal product form and the coherent state form of the Wigner operator are derived. Furthermore, the applications of the new forms of the Wigner operator are also presented, which are involved in deriving some new quantum operator formulas, in the coherent state generalization of the Moyal theorem, and in evaluating some quantum operators which corresponds to the given classical functions in the Weyl manner and vice versa.

Chinese Physics C•Jan 1, 1985•0 citations

Generalized Weyl Ordering and Nonlinear Coherent States

Fan Hong-Yi

In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl ordering operator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operator functions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship between normal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistent theory for NLCS.

Communications in Theoretical Physics•Dec 15, 2002•3 citations
We point out that there is a close connection between the Weyl correspondence and coherent state correspondence. By virtue of differential and integral method within normal ordered products we demonstrate that the essence of the Weyl correspondence is just coherent state correspondence in both boson and fermion cases. Furthermore, coherent state form and explicit operator form for the Wigner function are given. With these forms we can derive some important operator formulas from the Weyl correspondence. The Wigner function's zero-point value is also discussed.
Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector |q⟩ λ,ν of linear combination of the coordinate and momentum operator, (λQ + νP), where λ, ν are real numbers, and |q⟩ λν is complete, then the projector |q⟩ λν ⟨q| must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.
On the basis of the preceding paper we present some new applications of both the normal product form and the coherent state form of the Wigner operator, which involve deriving some new quantum operator formulas, giving the coherent state generalization of the Moyal theorem, evaluating some quantum operators which correspond to the given classical functions in the weyl manner and vice versa. Were it not for the Wigner operator's coherent state formulation given by us the above-mentioned calculations would be hard to perform.