Path integral solution of linear second order partial differential equations - II: elliptic, parabolic, and hyperbolic cases

摘要

The general theorem of LaChapelle [Path Integral Solution of Linear Second Order Partial Differential Equations, I. The General Case, preprint (2003)] is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial differential equations with Dirichlet/Neumann boundary conditions. The construction is checked by evaluating several known kernels for regions with planar and spherical boundaries. Some new calculational techniques are introduced. (C) 2004 Elsevier Inc. All rights reserved.