# Accession Number:

## ADA248451

# Title:

## Application of Gauge Theories to Enhance Numerical Solutions to Mixed Potential Integral Equations

# Descriptive Note:

## Technical rept.

# Corporate Author:

## TEXAS A AND M UNIV COLLEGE STATION

# Personal Author(s):

# Report Date:

## 1992-02-28

# Pagination or Media Count:

## 1.0

# Abstract:

The purpose of this research is to incorporate new advances in gauge techniques currently being researched in mathematical physics into numerical electromagnetic scattering routines with an emphasis on improving computation speeds and the versatility of current methods. During this past year we have developed a new scheme for solving two dimensional electromagnetic scattering problems in which the scatterer can be inhomogeneous. The Fourier transform path integral method FTPI is based on the Feynman path integral which is a Greens function for inhomogeneous regions. Although originally proposed in the late 40s path integral applications have been restricted to a limited variety of problems in quantum physics. This has been the case primarily because it is not a closed form expression but rather a sequence of nested integrals with infinite limits, which can only be evaluated by making stringent approximations that in turn Emit the geometries to which it is applicable. Our contribution has been that we were able to transform the original path integral into a form where the nested sequence because successive Fourier and inverse Fourier transforms. We can now take advantage of the well known fast Fourier transform FFT routines currently available to evaluate the path integral. Over the past year we have worked on solving electromagnetic field problems in one and two dimensions and on the dual problem of determining the scattering coefficients for a particle in the presence of a potential barrior. Because specialists in quantum mechanics have worked with the path integral in the past with only limited success we have also developed a FTPI method for computing energy levels in one, two and three dimensional quantum wells with general inhomogeneous potential levels.

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Electricity and Magnetism