WIAS Preprint No. 1851, (2013)

A random cloud model for the Schrödinger equation



Authors

  • Wagner, Wolfgang

2010 Mathematics Subject Classification

  • 35Q41 60J25 81Q05

Keywords

  • Schrödinger equation, probabilistic representation, stochastic particle model, Markov jump process

Abstract

The paper is concerned with the construction of a stochastic model for the spatially discretized time-dependent Schrödinger equation. The model is based on a particle system with a Markov jump evolution. The particles are characterized by a sign (plus or minus), a position (discrete grid) and a type (real or imaginary). The jumps are determined by the creation of offsprings. The main result is the construction of a family of complex-valued random variables such that their expected values coincide with the solution of the Schrödinger equation.

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