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

College Physics

A new representation of general linear quantum transform in phase space

Hao Zhi-ren

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Taking coordinate and momentum operators as basic operators of phase space,a new representation of general linear quantum transform is obtained,includinge transformation relationship expression,the condition of unitary transformation,the ordinary,normal product and anti-normal product expressions of transform operator.

Related papers

Mapping of classical canonical transformations to quantum unitary operators

Fan Hong‐Yi, Jack Vanderlinde

Classical linear transformations in coordinate-momentum phase space are mapped to unitary quantum-mechanical operators in Hilbert space to produce a generalization of squeeze operators. The classical to quantum transition is manifestly apparent in the derivation. The unitary operators are evaluated in the coherent-state representation using the ``integration within ordered products'' technique in the one- and two-mode cases. Application of these operators results in a new generalization of coherent states.

Physical Review A•Mar 1, 1989•61 citations

General Formalism for Mapping of Two-Mode Classical Canonical Transformations to Quantum Unitary operators

Hong-Yi Fan

Two types of canonical transformations in two-mode classical phase space are mapped into the quantum mechanical Hilbert space to produce some new normally ordered unitary operators. These operators are evaluated in the coordinate (momentum) representations using the "integration within ordered product" technique, and the mapping is manifestly apparent in the derivation. New generalized coherent states are constructed in terms of these operators, and the uncertainty relations for these states are analysed.

Communications in Theoretical Physics•Apr 1, 1992•5 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

Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics

Raoelina Andriambololona

We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions. Then we introduce the concept of isodispersion linear canonical transformation.

arXiv:1503.02449•International Journal of Applied Mathematics and Theoretical Physics•Jan 1, 2015•6 citations

QUANTUM PHASE SPACE THEORY BASED ON INTERMEDIATE COORDINATE-MOMENTUM REPRESENTATION

Hong-Yi Fan, Qin Guo

Through the Radon transformation of the normally ordered Wigner operator we introduce two mutually conjugate intermediate coordinate-momentum representations. Based on them we construct the appropriate quantum phase space theory which includes the new Wigner operator adapting to this space. We find that the new Wigner function's marginal distribution for a state |Ψ〉 is just the quantum tomogram of the state |Ψ〉.

Modern Physics Letters B•Nov 20, 2007•2 citations

Coordinate, Momentum and Dispersion operators in Phase space representation

Hanitriarivo Rakotoson, Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson +1 more

The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works. We begin in the introduction section with a recall about the concept of representation of operators on wave function spaces. Then, we show that in the case of the phase space representation the coordinate and momentum operators can be represented either with differential operators or with matrices. The explicit expressions of both the differential operators and matrices representations are established. Multidimensional generalization of the obtained results are performed and phase space representation of dispersion operators are given.

arXiv:1707.02223•Jul 5, 2017•5 citations
Classical linear transformations in coordinate-momentum phase space are mapped to unitary quantum-mechanical operators in Hilbert space to produce a generalization of squeeze operators. The classical to quantum transition is manifestly apparent in the derivation. The unitary operators are evaluated in the coherent-state representation using the ``integration within ordered products'' technique in the one- and two-mode cases. Application of these operators results in a new generalization of coherent states.
Two types of canonical transformations in two-mode classical phase space are mapped into the quantum mechanical Hilbert space to produce some new normally ordered unitary operators. These operators are evaluated in the coordinate (momentum) representations using the "integration within ordered product" technique, and the mapping is manifestly apparent in the derivation. New generalized coherent states are constructed in terms of these operators, and the uncertainty relations for these states are analysed.
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.
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions. Then we introduce the concept of isodispersion linear canonical transformation.
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works. We begin in the introduction section with a recall about the concept of representation of operators on wave function spaces. Then, we show that in the case of the phase space representation the coordinate and momentum operators can be represented either with differential operators or with matrices. The explicit expressions of both the differential operators and matrices representations are established. Multidimensional generalization of the obtained results are performed and phase space representation of dispersion operators are given.