Article
Licensed
Unlicensed
Requires Authentication
A class of probabilistic models for the Schrödinger equation
-
Wolfgang Wagner
Published/Copyright:
April 24, 2015
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
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Frontmatter
- Optimal switching problems under partial information
- A class of probabilistic models for the Schrödinger equation
- Computing the exit-time for a finite-range symmetric jump process
- Stochastic small perturbation based simulation technique for solving isotropic elastostatics equations
- Memory efficient lagged-Fibonacci random number generators for GPU supercomputing
- A limit theorem for average dimensions
Keywords for this article
Schrödinger equation;
probabilistic representation;
stochastic particle model;
piecewise deterministic
Markov process
Articles in the same Issue
- Frontmatter
- Optimal switching problems under partial information
- A class of probabilistic models for the Schrödinger equation
- Computing the exit-time for a finite-range symmetric jump process
- Stochastic small perturbation based simulation technique for solving isotropic elastostatics equations
- Memory efficient lagged-Fibonacci random number generators for GPU supercomputing
- A limit theorem for average dimensions
