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Abstract
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.
Keywords: Schrödinger equation; probabilistic representation; stochastic particle model; piecewise deterministic
Markov process
Received: 2014-11-6
Accepted: 2015-3-12
Published Online: 2015-4-24
Published in Print: 2015-6-1
© 2015 by De Gruyter
