摘要：

Hagedorn wave packets appear as the eigenstates of multidimensional harmonic oscillators, and are given by a polynomial times a Gaussian. We recognise the arising polynomials for normalised and unnormalised Hagedorn wave packets as generalised multivariate Hermite polynomials, which are not tensor products in general. We provide formulas for generating functions and ladder operators, and prove a direct connection to the Laguerre polynomials. As our main result, we show that the class of Hagedorn wave packets is invariant under the Wigner transform, and present an explanation for the product structure of normalised Hagedorn wave packets in phase space, which has recently been discovered.

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