Explicit formulas for the generalized Hermite polynomials in superspace

TL;DR

This paper derives explicit formulas for the generalized Hermite polynomials in superspace, which are eigenfunctions of a supersymmetric quantum model, using a determinantal approach based on the Hamiltonian's action.

Contribution

It introduces a new explicit determinantal formula for the superspace Hermite polynomials, expanding the understanding of eigenfunctions in supersymmetric models.

Findings

Explicit formulas for superspace Hermite polynomials derived

Determinantal expressions obtained for eigenfunctions

Triangular action of Hamiltonian on supermonomials established

Abstract

We provide explicit formulas for the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in superspace. The construction relies on the triangular action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions.