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Efficient simulation of the Schrödinger equation with a piecewise constant positive potential

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  • Yang, Xuxin
  • Rasila, Antti
  • Sottinen, Tommi

Abstract

We introduce a new method for the Monte Carlo simulation of a weak solution of the Schrödinger-type equation where the potential is piecewise constant and positive. The method, called the killing walk-on-spheres algorithm, combines the classical walk-on-spheres algorithm with killing that can be determined by using panharmonic measures. This paper continues our earlier work in which simulation of the solutions of the Yukawa and the Helmholtz partial differential equations were developed.

Suggested Citation

  • Yang, Xuxin & Rasila, Antti & Sottinen, Tommi, 2019. "Efficient simulation of the Schrödinger equation with a piecewise constant positive potential," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 315-323.
    • Handle: RePEc:eee:matcom:v:166:y:2019:i:c:p:315-323
    DOI: 10.1016/j.matcom.2019.05.012
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    References listed on IDEAS

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    1. Deaconu, M. & Herrmann, S. & Maire, S., 2017. "The walk on moving spheres: A new tool for simulating Brownian motion’s exit time from a domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 28-38.
    2. Xuxin Yang & Antti Rasila & Tommi Sottinen, 2017. "Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 589-602, June.
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