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Volume 11
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10.3390/sym11030344
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Article

Quasiprobability Distribution Functions from Fractional Fourier Transforms

by
Jorge A. Anaya-Contreras
1,
Arturo Zúñiga-Segundo
1 and
Héctor M. Moya-Cessa
2,*
1
Instituto Politécnico Nacional, ESFM, Departamento de Física, Edificio 9, Unidad Profesional Adolfo López Mateos, Ciuadad de México CP 07738, Mexico
2
Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro 1, Santa María Tonantzintla, Puebla 72840, Mexico
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(3), 344; https://doi.org/10.3390/sym11030344
Submission received: 13 February 2019 / Revised: 1 March 2019 / Accepted: 5 March 2019 / Published: 7 March 2019
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
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Abstract

We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual Fourier transform. We end the manuscript by showing a way in which the distribution we are introducing may be reconstructed by using atom-field interactions.
Keywords: quasiprobability distribution functions; fractional Fourier transform; reconstruction of the wave function quasiprobability distribution functions; fractional Fourier transform; reconstruction of the wave function

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MDPI and ACS Style

Anaya-Contreras, J.A.; Zúñiga-Segundo, A.; Moya-Cessa, H.M. Quasiprobability Distribution Functions from Fractional Fourier Transforms. Symmetry 2019, 11, 344. https://doi.org/10.3390/sym11030344

AMA Style

Anaya-Contreras JA, Zúñiga-Segundo A, Moya-Cessa HM. Quasiprobability Distribution Functions from Fractional Fourier Transforms. Symmetry. 2019; 11(3):344. https://doi.org/10.3390/sym11030344

Chicago/Turabian Style

Anaya-Contreras, Jorge A., Arturo Zúñiga-Segundo, and Héctor M. Moya-Cessa. 2019. "Quasiprobability Distribution Functions from Fractional Fourier Transforms" Symmetry 11, no. 3: 344. https://doi.org/10.3390/sym11030344

APA Style

Anaya-Contreras, J. A., Zúñiga-Segundo, A., & Moya-Cessa, H. M. (2019). Quasiprobability Distribution Functions from Fractional Fourier Transforms. Symmetry, 11(3), 344. https://doi.org/10.3390/sym11030344

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