The Gaussian Wave Packet Transform via Quadrature Rules
Abstract
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented. Including a rigorous error analysis, the variants of the wave packet transform are then derived by a discretisation of the Fourier integral via different quadrature rules. Based on Gauss--Hermite quadrature, we introduce a new representation of Gaussian wave packets in which the number of basis functions is significantly reduced. Numerical experiments in 1D illustrate the theoretical results.
Cite
@article{arxiv.2010.03478,
title = {The Gaussian Wave Packet Transform via Quadrature Rules},
author = {Paul Bergold and Caroline Lasser},
journal= {arXiv preprint arXiv:2010.03478},
year = {2023}
}
Comments
Version 3: Additional references, extension of the theoretical and numerical results and some corrections to version 2