An Introduction to the Application of Feynman Path Integrals to Sound Propagation in the Ocean.
Abstract
We review and unify those applications and techniques associated with Feynman's theory of path integrals which have been found relevant for sound propagation in the ocean. After giving an introductory discussion of functional integrals in general and Feynman path integrals in particular, we derive several path integral representations for the solutions to the two- and three-dimensional parabolic equations. The analogies which exist between sound propagation, the nonrelativistic quantum mechanics of a point particle, and Brownian motion are considered. Next we use the path integral to derive several methods of approximation including perturbation theory, the Rytov approximation, ray acoustics, and straight-line geometric optics. The formalism is then applied to the problem of developing algorithms for numerically solving the parabolic equation. After developing path integral representations for the solution to the Helmholtz equation, we give an extensive discussion of the parabolic approximation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 06, 1978
- Accession Number
- ADA060734
Entities
People
- D. R. Palmer
Organizations
- United States Naval Research Laboratory