Mehta's eigenvectors for the finite Hartely transform

Abstract

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.