An invariant class of wave packets for the Wigner transform
Mathematical Physics
2025-03-25 v3 Classical Analysis and ODEs
math.MP
Abstract
Generalised Hagedorn wave packets appear as exact solutions of Schr\"odinger equations with quadratic, possibly complex, potential, and are given by a polynomial times a Gaussian. We show that the Wigner transform of generalised Hagedorn wave packets is a wave packet of the same type in phase space. The proofs build on a parametrisation via Lagrangian frames and a detailed analysis of the polynomial prefactors, including a novel Laguerre connection. Our findings directly imply the recently found tensor product structure of the Wigner transform of Hagedorn wave packets.
Cite
@article{arxiv.1505.06192,
title = {An invariant class of wave packets for the Wigner transform},
author = {Helge Dietert and Johannes Keller and Stephanie Troppmann},
journal= {arXiv preprint arXiv:1505.06192},
year = {2025}
}
Comments
19 pages, 3 figures: This version focuses on the Wigner transform and dropped details on the orthogonal polynomials