An invariant class of wave packets for the Wigner transform

Abstract

Generalised Hagedorn wave packets appear as exact solutions of Schrödinger 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.

19 pages, 3 figures: This version focuses on the Wigner transform and dropped details on the orthogonal polynomials

References in corpus (1)

• Generating Function and a Rodrigues Formula for the Polynomials in $d$-Dimensional Semiclassical Wave Packets

Cited by in corpus (4)

• Computing quantum dynamics in the semiclassical regime
• The Hagedorn--Hermite Correspondence
• Stable evaluation of Gaussian radial basis functions using Hermite polynomials
• Generating Function and a Rodrigues Formula for the Polynomials in $d$-Dimensional Semiclassical Wave Packets