Hagedorn wavepackets in time-frequency and phase space
This work provides theoretical tools for analyzing Hagedorn wavepackets in time-frequency analysis, but the contribution is incremental for mathematicians working in harmonic analysis.
The authors derive explicit formulas and recurrence relations for the Wigner and FBI transforms of Hagedorn wavepackets, showing their relation to Laguerre polynomials. No concrete numerical results are provided.
The Hermite functions are an orthonormalbasis of the space of square integrable functions with favourable approximation properties. Allowing for a flexible localization in position and momentum, the Hagedorn wavepackets generalize the Hermite functions also to several dimensions. Using Hagedorn's raising and lowering operators, we derive explicit formulas and recurrence relations for the Wigner and FBI transform of the wavepackets and show their relation to the Laguerre polyomials.