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

Jilin Normal University Journal

Fourier Transform Operator between the Coordinate and Momentum Eigenstates

Zhang Bing-yun

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Three non-symmetric projective operators were made by coordinate,momentum eigenstates and coherent states.By IWOP technology,three non-symmetric projective operators were the same Fourier transform operator.This operator could realize the Fourier transform between the coordinate and momentum eigenstates,and the unitary transformation between the coordinate and momentum operators.

Related papers

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

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.

Acta Physica Sinica•Jan 1, 2008•1 citation

The Parity Operator and the Fourier Transform Operator

Saul T. Epstein

Explicit formulas, in terms of coordinate and momentum operators, are given for the parity operator and the Fourier-transform operator.

American Journal of Physics•May 1, 1965•5 citations

Normally ordering the Dirac's radial momentum operator and the power of radial coordinate operators by virtue of the IWOP technique

Hong-Yi Fan, Junhua Chen

By virtue of the technique of integration within an ordered product of operators we derive the normal ordering expansion of the Dirac's radial momentum operator. To realize this goal, we also derive some operator identities of the power of radial coordinate operators. They are useful in calculating expectation values in the coherent state.

Journal of Physics A Mathematical and General•Dec 5, 2001•9 citations

Coherent states and projective representation of the linear canonical transformations

Ingrid C. Daubechies

Using a family of coherent state representations we obtain in a natural and coordinate-independent way an explicit realization of a projective unitary representation of the symplectic group. Dequantization of these operators gives us the corresponding classical functions.

Journal of Mathematical Physics•Jun 1, 1980•23 citations

Quantum-Mechanical Unitary Operators Gained via Integrations over a Type of Ket-Bra Operators

Fan Hong-Yi

Applying the technique of integration within ordered product (IWOP) to a type of ket-bra operators which are in integral form in coordinate representation, we derive unitary normally ordered quantum-mechanical images of real symmetric transformations in classical coordinate space, which provide us with a convenient approach to constructing the corresponding coherent states. Some examples showing the physical applications of this kind of unitary images are presented.

Europhysics Letters (EPL)•Jan 21, 1992•2 citations

Quantum entangled fractional Fourier transform based on the IWOP technique

Ke Zhang, Lanlan Li, Pan-Pan Yu +3 more

In our previous papers, the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics, and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform. The core function of the coordinate–momentum exchange operators in the addition law of fractional Fourier transform was analyzed too. In this paper, the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators (IWOP) are used to establish the entanglement fractional Fourier transform theory to the extent of quantum. A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Chinese Physics B•Jul 5, 2022•4 citations
Three non-symmetric projective operators were made by coordinate,momentum eigenstates and coherent states.By IWOP technology,three non-symmetric projective operators were the same Fourier transform operator.This operator could realize the Fourier transform between the coordinate and momentum eigenstates,and the unitary transformation between the coordinate and momentum operators.
In our previous papers, the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics, and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform. The core function of the coordinate–momentum exchange operators in the addition law of fractional Fourier transform was analyzed too. In this paper, the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators (IWOP) are used to establish the entanglement fractional Fourier transform theory to the extent of quantum. A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.