The Dunkl-Fokker-Planck Equation in $1+1$ Dimensions
R. D. Mota, D. Ojeda-Guill\'en, and M. A. Xicot\'encatl
TL;DR
This paper introduces a generalized Fokker-Planck equation using Dunkl derivatives in 1+1 dimensions, solving for specific potentials and connecting to Wigner-Dunkl supersymmetry.
Contribution
It develops the Dunkl-Fokker-Planck equation, derives its eigenvalues, and links it to supersymmetry in quantum mechanics.
Findings
Eigenvalues for harmonic oscillator with Dunkl derivatives
Solutions for centrifugal-type potential
Connection to Wigner-Dunkl supersymmetry
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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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Nuclear physics research studies · Neutrino Physics Research