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A time–splitting for the semiclassical Schrödinger equation

by V. Gradinaru and G. A. Hagedorn

(Report number 2012-15)

Abstract
We propose a new algorithm for solving the semiclassical time–dependent Schrödinger equation. The algorithm is based on semiclassical wavepackets. Convergence is proved to be quadratic in the time step and linear in the semiclassical parameter E. To the authors' best knowledge, all earlier algorithms had errors that grew as the semiclassical parameter was decreased.

Keywords:

@Techreport{GH12_458,
  author = {V. Gradinaru and G. A. Hagedorn},
  title = {A time–splitting for the semiclassical Schr\"odinger equation},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2012-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2012/2012-15.pdf },
  year = {2012}
}

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