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Eulerian Gaussian beams for Schrdinger equations in the semi-classical regime

Shing-Yu Leung Jianliang Qian

General Methematics mathscidoc:1912.43179

Journal of Computational Physics, 228, (8), 2951-2977, 2009.5
We propose Gaussian-beam based Eulerian methods to compute semi-classical solutions of the Schrdinger equation. Traditional Gaussian beam type methods for the Schrdinger equation are based on the Lagrangian ray tracing. Based on the first Eulerian Gaussian beam framework proposed in Leung et al.[S. Leung, J. Qian, R. Burridge, Eulerian Gaussian beams for high frequency wave propagation, Geophysics 72 (2007) SM61SM76], we develop a new Eulerian Gaussian beam method which uses global Cartesian coordinates, level-set based implicit representation and Liouville equations. The resulting method gives uniformly distributed phases and amplitudes in phase space simultaneously. To obtain semi-classical solutions to the Schrdinger equation with different initial wave functions, we only need to slightly modify the summation formula. This yields a very efficient method for computing semi
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@inproceedings{shing-yu2009eulerian,
  title={Eulerian Gaussian beams for Schrdinger equations in the semi-classical regime},
  author={Shing-Yu Leung, and Jianliang Qian},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112756952292739},
  booktitle={Journal of Computational Physics},
  volume={228},
  number={8},
  pages={2951-2977},
  year={2009},
}
Shing-Yu Leung, and Jianliang Qian. Eulerian Gaussian beams for Schrdinger equations in the semi-classical regime. 2009. Vol. 228. In Journal of Computational Physics. pp.2951-2977. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112756952292739.
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