An invariant class of wave packets for the Wigner transform

Autor:	Dietert, Helge, Keller, Johannes, Troppmann, Stephanie
Rok vydání:	2015
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs 81R30 65R10 81S10
Druh dokumentu:	Working Paper
Popis:	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. Comment: 19 pages, 3 figures: This version focuses on the Wigner transform and dropped details on the orthogonal polynomials
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1505.06192 Zobrazit plný text záznamu View this record from Arxiv