Kinetic and Related Models (KRM)

A random cloud model for the Schrödinger equation

Pages: 361 - 379, Volume 7, Issue 2, June 2014      doi:10.3934/krm.2014.7.361

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Wolfgang Wagner - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39 - 10117 Berlin, Germany (email)

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 offspring. 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.

Keywords:  Schrödinger equation, probabilistic representation, stochastic particle model, Markov jump process.
Mathematics Subject Classification:  Primary: 35Q41, 60J25; Secondary: 81Q05.

Received: October 2013;      Revised: January 2014;      Available Online: March 2014.