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Hagedorn wavepackets in phase space

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The Hermite functions are close to heart of numerical analysis and mathematical physics, forming an orthonormalbasis of the space of square integrable functions with favourable approximation properties. The Hagedorn wave packets generalize the Hermite functions to several dimensions, allowing for a flexible localization in position and momentum, while satisfying a three term recurrence relation and a Rodrigues formula. We review known and new properties of Hagedorn wavepackets and use them for a Galerkin discretization of Schrödinger type equations from the phase space point of view.

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