A random walk model for the Schrodinger equation

被引：2
作者：
Wagner, Wolfgang [1 ]
机构：
[1] Weierstrass Inst Appl Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2018年 / 143卷
关键词：
Schrodinger equation; Probabilistic representation; Random walk model; Piecewise deterministic Markov process; WEIGHTED PARTICLE METHOD; RANDOM CLOUD MODEL; SIMULATION;
D O I：
10.1016/j.matcom.2016.07.012
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
A random walk model for the spatially discretized time-dependent Schrodinger equation is constructed. The model consists of a class of piecewise deterministic Markov processes. The states of the processes are characterized by a position and a complex-valued weight. Jumps occur both on the spatial grid and in the space of weights. Between the jumps, the weights change according to deterministic rules. The main result is that certain functionals of the processes satisfy the Schrodinger equation. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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页码：138 / 148
页数：11
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