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The Dunkl–Fokker–Planck Equation in \(1+1\) Dimensions

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Abstract

By replacing the spatial derivative with the Dunkl derivative, we generalize the Fokker-Planck equation in (1+1) dimensions. We obtain the Dunkl–Fokker–Planck eigenvalues equation and solve it for the harmonic oscillator plus a centrifugal-type potential. Furthermore, when the drift function is odd, we reduce our results to those of the recently developed Wigner–Dunkl supersymmetry.

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Acknowledgements

This work was partially supported by SNII-Mexico, COFAA-IPN, EDI-IPN, CGPI-IPN Project Numbers 20230633, 20230732, and CONAHCYT-Mexico grant CB-2017-2018-A1-S-30345. We appreciate the observations made by the anonymous referee to improve our work.

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Authors and Affiliations

  1. Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Alc. Coyoacán, C.P. 04430, Ciudad de México, Mexico

    R. D. Mota

  2. Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Alc. Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico

    D. Ojeda-Guillén

  3. Departamento de Matemáticas, Centro de Investigación y Estudios Avanzados del IPN, C.P. 07360, Ciudad de México, Mexico

    M. A. Xicoténcatl

Authors
  1. R. D. Mota
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  2. D. Ojeda-Guillén
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  3. M. A. Xicoténcatl
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All authors contributed equally to the paper.

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Correspondence to D. Ojeda-Guillén.

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Mota, R.D., Ojeda-Guillén, D. & Xicoténcatl, M.A. The Dunkl–Fokker–Planck Equation in \(1+1\) Dimensions. Few-Body Syst 65, 25 (2024). https://doi.org/10.1007/s00601-024-01898-1

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