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We show that a constant-potential time-independent Schr\"odinger equationwith Dirichlet boundary data can be reformulated as a Laplace equation withDirichlet boundary data. With this reformulation, which we call the Duffincorrespondence, we provide a classical Walk On Spheres (WOS) algorithm forMonte Carlo simulation of the solutions of the boundary value problem. Wecompare the obtained Duffin WOS algorithm with existing modified WOSalgorithms.

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