GWPTools: An extensible Wolfram Language framework for time-dependent Gaussian wave packet dynamics
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.