2024/06/15 by Fethi Bouzeffour, Bouzeffour, Fethi
Mathematics · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2406.19410
openalex publication_date 2024/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a novel approach for evaluating analytical eigenfunctions of the finite Hartley transform. The approach is based on the use of N=1/2-supersymmetric quantum mechanics as a fundamental tool, which builds on the key observation that the Hartley transform commutes with the supercharge operator. Using the intertwining operator between the Hartley transform and the finite Hartley transform, our approach provides an overcomplete basis of eigenvectors expressed in terms of supersymmetric Hermite polynomials.