Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction

Details Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction

2004-05-10

arxiv.org/abs/math-ph/0405031v1

Physics

Mathematical Physics

40 pages

Scientific paper

10.1016/j.aop.2004.06.007

A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schr\"{o}dinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette.

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