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

Xuxin Yang, Antti Rasila and Tommi Sottinen

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 166, issue C, 315-323

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.

Keywords: Brownian motion; Killing walk-on-spheres; Harmonic measure; Numerical algorithm; Yukawa equation; Schrödinger equation (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:166:y:2019:i:c:p:315-323

DOI: 10.1016/j.matcom.2019.05.012

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