Gaussian beam methods for the Schrödinger equation with discontinuous potentials

@article{Jin2014GaussianBM,
  title={Gaussian beam methods for the Schr{\"o}dinger equation with discontinuous potentials},
  author={Shi Jin and Dongming Wei and Dongsheng Yin},
  journal={J. Computational Applied Mathematics},
  year={2014},
  volume={265},
  pages={199-219}
}

• Shi Jin, Dongming Wei, Dongsheng Yin
• Published 2014 in J. Computational Applied Mathematics
• DOI:10.1016/j.cam.2013.09.028

We propose Eulerian and Lagrangian Gaussian beam methods for the Schrödinger equation with discontinuous potentials. At the quantum barriers where the potential is discontinuous, we derive suitable interface conditions to account for quantum scattering information. These scattering interface conditions are then built into the numerical fluxes in the Eulerian level set formulation of the Gaussian beam methods, and are also used in the Lagrangian formulation, including an interface condition for… CONTINUE READING

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