An invariant class of wave packets for the Wigner transform
Autor: | Dietert, Helge, Keller, Johannes, Troppmann, Stephanie |
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Rok vydání: | 2015 |
Předmět: | |
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 |
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