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- Title
The Gaussian wave packet transform via quadrature rules.
- Authors
Bergold, Paul; Lasser, Caroline
- 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 discretization 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.
- Subjects
UNITED States. Federal Bureau of Investigation; WAVE packets; GAUSSIAN quadrature formulas; FOURIER integrals; GAUSSIAN function; SCHRODINGER equation
- Publication
IMA Journal of Numerical Analysis, 2024, Vol 44, Issue 3, p1785
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drad049