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

Results in Physics

A Fourier transform differentiator operator

Blanca L. Moreno-Ley, Jorge Andres Anaya-Contreras, Arturo Zúñiga-Segundo, H. M. Moya-Cessa

Published Nov 25, 2023• 2 citations
Publisher

Abstract

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral

DOI
10.1016/j.rinp.2023.107217

Related papers

Squeeze operators in classical scenarios

Jorge Andres Anaya-Contreras, Arturo Zúñiga-Segundo, Francisco Soto +2 more

We analyse the paraxial field propagation in the realm of classical optics, showing that it can be written as the action of the fractional Fourier transform, followed by the squeeze operator applied to the initial field. Secondly, we show that a wavelet transform may be viewed as the application of a displacement and squeeze operator onto the mother wavelet function.

arXiv:1901.05491•Jan 16, 2019•0 citations

Squeeze Operators in Classical Scenarios

Jorge Andres Anaya-Contreras, Arturo Zúñiga-Segundo, Francisco Soto +2 more

We analyse the paraxial field propagation in the realm of classical optics, showing that it can be written as the action of the fractional Fourier transform, followed by the squeeze operator applied to the initial field.Secondly, we show that a wavelet transform may be viewed as the application of a displacement and squeeze operator onto the mother wavelet function.

Applied Mathematics & Information Sciences•Mar 1, 2019•2 citations

On the Scaled Fractional Fourier Transformation Operator

Fan Hong‐Yi, Liyun Hu

Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched.

Chinese Physics Letters•Feb 1, 2008•10 citations

MÉTODO DE OPERADORES EM MECÂNICA QUÂNTICA

Lucas Henrique Elias Vieira, Petrus Henrique Ribeiro dos Anjos

This paper will introduce and discuss the method of Operators in Quantum Mechanics. This presentation will be mathematically rigorous, but also physically motivate the definitions and propositions established.

•Aug 1, 2015•0 citations

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

CLASSICAL OPTICAL TRANSFORMS STUDIED IN THE CONTEXT OF QUANTUM OPTICS VIA THE ROUTE OF DEVELOPING DIRAC'S SYMBOLIC METHOD

Hong-Yi Fan, Lu Hai-Liang

Via the route of developing Dirac's symbolic method and following Dirac's assertion: "⋯ for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory", we find the generalized Fresnel operator (GFO) corresponding to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in quantum optics. With the aid of entangled state representation the entangled Fresnel transform is proposed; new eigenfunctions of the complex fractional Fourier transform and fractional Hankel transform are obtained; the two-variable Hermite eigenmodes of light propagation are used in studying the Talbot effect in quadratic-index media; the complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Moreover, quantum optical version of classical z-transforms is obtained on the basis of the eigenvector of creation operator. Throughout our discussions, the coherent state, squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used.

International Journal of Modern Physics B•Feb 20, 2005•19 citations
By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral
Via the route of developing Dirac's symbolic method and following Dirac's assertion: "⋯ for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory", we find the generalized Fresnel operator (GFO) corresponding to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in quantum optics. With the aid of entangled state representation the entangled Fresnel transform is proposed; new eigenfunctions of the complex fractional Fourier transform and fractional Hankel transform are obtained; the two-variable Hermite eigenmodes of light propagation are used in studying the Talbot effect in quadratic-index media; the complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Moreover, quantum optical version of classical z-transforms is obtained on the basis of the eigenvector of creation operator. Throughout our discussions, the coherent state, squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used.