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.
Original language | English |
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Pages (from-to) | 589-602 |
Number of pages | 14 |
Journal | Methodology and Computing in Applied Probability |
Volume | 19 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jun 2017 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Brownian motion
- Monte Carlo simulation
- Numerical algorithm
- Linearized Poisson–Boltzmann equation
- Helmholtz equation
- Walk On Spheres algorithm