Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 450, Issue 2, Pages 1317-1332Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2016.12.041
Keywords
Hagedorn wave packets; Wigner functions; Multivariate polynomials; Hermite functions
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Funding
- UK Engineering and Physical Sciences Research Council (EPSRC) [EP/H023348/1]
- DFG-Collaborative Research Center [TRR 109]
- graduate program TopMath of the Elite Network of Bavaria
- Engineering and Physical Sciences Research Council [1220107] Funding Source: researchfish
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Generalised Hagedorn wave packets appear as exact solutions of Schrodinger 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. (C) 2016 Elsevier Inc. All rights reserved.
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