On computer simulation of Feynman-Kac path-integrals
type: Item
instance of: scholarly article
title: On computer simulation of Feynman-Kac path-integrals
zbMATH Open document ID: 0853.65132
DOI: 10.1016/0377-0427(95)00170-0
published in: Journal of Computational and Applied Mathematics
publication date: 1997-01-05T00:00:00Z
review text: Using the Feynman-Kac formula \(u(t, x)= E_x \exp\{- \int^t_0 V(X(s)) ds\}\) for the solution of a diffusion version of the generalized Schrödinger equation \(\partial u/\partial t= Hu\), \(u(0, x)= f(x)\), quantum mechanical systems are studied. The generalization involves the introduction of a new potential as a perturbation of \(V\), \(U(x)= V(x)- {1\over 2} {\Delta\varphi(x)\over \varphi(x)}\). Various choices of \(\varphi\) correspond to important sampling techniques. As examples the one-dimensional harmonic oscillator and hydrogen atom are analyzed by the Feynman-Kac formula and important (space and time averages) technique. By combining the important sampling techniques with parallel computing quantum mechanical particle systems may be treated.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 908332
zbMATH Keywords: Feynman-Kac path-integrals
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: harmonic oscillator
zbMATH Keywords: hydrogen atom
zbMATH Keywords: parallel computing
zbMATH Keywords: quantum mechanical particle systems
author: A. Korzeniowski
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00170-0
OpenAlex ID: W2107433589
cites work: On Simulating Wiener Integrals and Their Expectations
cites work: Q3139889
cites work: Schrödinger semigroups
description: scientific article; zbMATH DE number 908332