Path integral solution of the Dirichlet problem
type: Item
instance of: scholarly article
title: Path integral solution of the Dirichlet problem
zbMATH Open document ID: 0939.58013
author: J. Lachapelle
published in: Annals of Physics
publication date: 1999-09-12T00:00:00Z
review text: The paper elaborates a further development of a functional integration scheme suggested by Cartier and De Witt-Morette. In particular, results of the paper together with Cartier/De Witt-Morette's results provide the functional integral solution of elliptic and parabolic second order PDE's. The path integral solution of the Dirichlet problem in terms of first exit time is constructed and then applied to calculate the fixed-energy point-to-point transition amplitude both in configuration and phase space. It is shown that the Fourier transform in energy of the fixed-energy point-to-point transition amplitude gives the well-known transition amplitude obtained by using physical principles based on Feynman's original reasoning. The WKB approximation is also calculated.
Mathematics Subject Classification ID: 58D30
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 81S40
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 46N50
zbMATH DE Number: 1217308
zbMATH Keywords: functional integration
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: stochastic approach
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: transition amplitude
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
cites work: A new perspective on functional integration
cites work: Hamiltonian Path-Integral Methods
cites work: Functional Integration and Partial Differential Equations. (AM-109)
cites work: Q4086524
cites work: Path integration in phase space
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description: scientific article; zbMATH DE number 1217308