Journal
JOURNAL OF CHEMICAL PHYSICS
Volume 136, Issue 1, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.3671978
Keywords
quantum theory; Schrodinger equation
Funding
- Early Career Fellowship
- Leverhulme Trust
- EPSRC [EP/G00224X]
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We propose a method for dealing with the problem of linear dependence in quantum dynamics simulations employing over-complete Gaussian wavepacket (GWP) basis sets. In particular, by periodically projecting out redundant basis functions using the matching pursuit algorithm whilst simultaneously introducing GWPs which avoid linear dependence with the current basis set, we find that numerical conditioning of the equations-of-motion can be readily controlled. In applications to particle tunnelling in one- and two-dimensional potentials, this method allows us to reproduce the exact quantum-mechanical results with fewer GWP basis functions than similar calculations with non-adaptive basis sets, a result which we trace back to the improved energy conservation of our adaptive approach. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3671978]
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