A class of probabilistic models for the Schrödinger equation

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813153492.pdf (182.29 KB)

Date

2014

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1982

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WIAS Preprints

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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik

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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.

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Keywords

Schrödinger equation, probabilistic representation, stochastic particle model, piecewise deterministic Markov process

Keywords GND

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Report

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publishedVersion

URI

https://doi.org/10.34657/1763
 https://oa.tib.eu/renate/handle/123456789/2839

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Mathematik
WIAS Preprints

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