A random cloud model for the Schrödinger equation
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 35Q41 60J25 81Q05
- Schrödinger equation, probabilistic representation, stochastic particle model, Markov jump process
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.