  We show that a constant-potential time-independent Schr\"odinger 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.
