A class of probabilistic models for the Schrödinger equation
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 35Q41 60J25 81Q05
- Schrödinger equation, probabilistic representation, stochastic particle model, piecewise deterministic Markov process
A class of stochastic particle models for the spatially discretized time-dependent Schrödinger equation is constructed. Each particle is characterized by a complex-valued weight and a position. The particle weights change according to some deterministic rules between the jumps. The jumps are determined by the creation of offspring. The main result is that certain functionals of the particle systems satisfy the Schrödinger equation. The proofs are based on the theory of piecewise deterministic Markov processes.
- Monte Carlo Methods Appl., 21 (2015) pp. 121--137.