WALK ON SPHERES ALGORITHMS FOR HELMHOLTZ AND LINEARIZED POISSON-BOLTZMANN EQUATIONS

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 algorithm for Monte Carlo simulation of the solutions of the boundary value problem.

This is joint work with A. Rasila and X. Yang.