An Effective Field Theory Approach to the One-Dimensional Scattering Problem
PublisherThe University of Arizona.
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AbstractWe demonstrate the effective field theory (EFT) principle by approximating the coefficient of reflection resulting from a one-dimensional finite square barrier potential with a series of Dirac delta functions up to second order in derivative. The explicit conditions for energy, E, finite square barrier potential height, V0, and finite square barrier potential width, a, wherein the approximation is valid are provided. We show that the inclusion of the second order derivative with the Dirac delta function in the series improves the agreement of the result. Generally, at any order the agreement between the approximation and the exact result deteriorates as E or the dimensionless quantity V₀a increases. In addition, at a given E or V₀a value the agreement improves as the order increases. Our results suggest that a more accurate approximation will occur with the addition of further derivatives of the Dirac delta function to the approximating potential, which is in line with the underlying assumptions behind the use of EFTs.
Degree ProgramHonors College