GWPTools: An extensible Wolfram Language framework for time-dependent Gaussian wave packet dynamics
Abstract
Gaussian wave packets provide an exact analytical foundation for modeling time-dependent quantum phenomena, effectively bridging the gap between classical trajectories and full quantum mechanics. We introduce GWPTools, a highly extensible Wolfram Language framework designed to compute exact time-dependent Gaussian wave packet dynamics using a unified symbolic-numeric architecture. Built upon a robust ``parameter bus'' and polymorphic dispatch, the software serves as an interactive pedagogical tool for exploring quantum theory and an exact algebraic engine for rigorously benchmarking numerical grid-based and trajectory methodologies. Version 1.0.0 focuses on exact time evolution in driven one-dimensional quadratic potentials. Native extensions into quantum hydrodynamics and phase space representations enable exact energy decompositions, analytical Bohmian trajectories, and symbolic derivations of quasi-probability distributions and information metrics. We demonstrate the framework's modular scalability by prototyping interference in superpositions, open-system decoherence, and coupled two-dimensional oscillators. Ultimately, these capabilities establish a versatile foundation for maximizing the reach of exact analytical modeling toward increasingly complex driven quantum systems.
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BibTeX
@misc{maddox2026gwptools,
title = {{GWPTools: An extensible Wolfram Language framework for time-dependent Gaussian wave packet dynamics}},
author = {Jeremy B. Maddox and Ismail Giliani and Carter M. Heck and Connor S. Mattingly},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17683},
eprint = {2610.17683},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17683},
}
RIS
TY - UNPB
TI - GWPTools: An extensible Wolfram Language framework for time-dependent Gaussian wave packet dynamics
AU - Jeremy B. Maddox
AU - Ismail Giliani
AU - Carter M. Heck
AU - Connor S. Mattingly
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17683
UR - https://arxiv.org/abs/2610.17683
AB - Gaussian wave packets provide an exact analytical foundation for modeling time-dependent quantum phenomena, effectively bridging the gap between classical trajectories and full quantum mechanics. We introduce GWPTools, a highly extensible Wolfram Language framework designed to compute exact time-dependent Gaussian wave packet dynamics using a unified symbolic-numeric architecture. Built upon a robust ``parameter bus'' and polymorphic dispatch, the software serves as an interactive pedagogical tool for exploring quantum theory and an exact algebraic engine for rigorously benchmarking numerical grid-based and trajectory methodologies. Version 1.0.0 focuses on exact time evolution in driven one-dimensional quadratic potentials. Native extensions into quantum hydrodynamics and phase space representations enable exact energy decompositions, analytical Bohmian trajectories, and symbolic derivations of quasi-probability distributions and information metrics. We demonstrate the framework's modular scalability by prototyping interference in superpositions, open-system decoherence, and coupled two-dimensional oscillators. Ultimately, these capabilities establish a versatile foundation for maximizing the reach of exact analytical modeling toward increasingly complex driven quantum systems.
ER -