A new approach to the star-genvalue equation

TL;DR

This paper introduces a novel method to solve the star-genvalue equation by relating it to the quantum Hamiltonian eigenproblem using Weyl-type representations and the cross-Wigner transform.

Contribution

It provides a new approach that expresses star-genvalue eigenvalues and eigenfunctions through the quantum Hamiltonian eigenproblem, utilizing Weyl-type representations and the cross-Wigner transform.

Findings

Eigenvalues and eigenfunctions can be fully expressed via the quantum Hamiltonian eigenproblem.

Uses Weyl-type representation of the star-product.

Employs the cross-Wigner transform as an intertwining operator.

Abstract

We show that the eigenvalues and eigenfunctions of the stargenvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonian. Our method makes use of a Weyl-type representation of the star-product and of the properties of the cross-Wigner transform, which appears as an intertwining operator.