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Related Experiment Video

Updated: May 25, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Linear dependence and energy conservation in Gaussian wavepacket basis sets.

Scott Habershon¹

¹Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom. scott.habershon@bristol.ac.uk

The Journal of Chemical Physics

|January 14, 2012

Summary

We developed an adaptive method using Gaussian wavepacket (GWP) basis sets to control linear dependence in quantum dynamics simulations. This approach improves numerical stability and accuracy, reducing the number of basis functions needed for simulations.

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Area of Science:

Quantum mechanics
Computational chemistry
Theoretical physics

Background:

Over-complete Gaussian wavepacket (GWP) basis sets can lead to linear dependence issues in quantum dynamics simulations.
Controlling numerical conditioning is crucial for accurate simulations of quantum systems.

Purpose of the Study:

To develop and validate an adaptive method for managing linear dependence in GWP basis sets for quantum dynamics.
To improve the efficiency and accuracy of simulations by reducing basis set redundancy.

Main Methods:

Periodically projecting out redundant basis functions using the matching pursuit algorithm.
Introducing new Gaussian wavepackets (GWPs) that avoid linear dependence with the existing basis set.
Applying the adaptive method to simulations of particle tunneling in one- and two-dimensional potentials.

Main Results:

Successfully controlled the numerical conditioning of the equations-of-motion.
Reproduced exact quantum-mechanical results with fewer GWP basis functions compared to non-adaptive methods.
Observed improved energy conservation in simulations using the adaptive approach.

Conclusions:

The proposed adaptive method effectively addresses linear dependence in GWP basis sets for quantum dynamics.
The method enhances simulation accuracy and efficiency by optimizing basis set size.
Improved energy conservation is a key factor in the success of this adaptive strategy.