Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence

Abstract

We show that a constant-potential time-independent Schrödinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms.

14 pages, 5 figures

References in corpus (2)

• Hitting time for Bessel processes - walk on moving spheres algorithm (WoMS)
• Efficient simulation of Schrödinger equation with piecewise constant positive potential