Moreno-Ley, B.L.; Anaya-Contreras, J.A.; Zúñiga-Segundo, A.; Moya-Cessa, H.M. A Fourier Transform Differentiator Operator. Results in Physics 2024, 56, 107217, doi:10.1016/j.rinp.2023.107217.
Moreno-Ley, B.L.; Anaya-Contreras, J.A.; Zúñiga-Segundo, A.; Moya-Cessa, H.M. A Fourier Transform Differentiator Operator. Results in Physics 2024, 56, 107217, doi:10.1016/j.rinp.2023.107217.
Moreno-Ley, B.L.; Anaya-Contreras, J.A.; Zúñiga-Segundo, A.; Moya-Cessa, H.M. A Fourier Transform Differentiator Operator. Results in Physics 2024, 56, 107217, doi:10.1016/j.rinp.2023.107217.
Moreno-Ley, B.L.; Anaya-Contreras, J.A.; Zúñiga-Segundo, A.; Moya-Cessa, H.M. A Fourier Transform Differentiator Operator. Results in Physics 2024, 56, 107217, doi:10.1016/j.rinp.2023.107217.
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.
Keywords
fourier transform; number states
Subject
Physical Sciences, Quantum Science and Technology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
