An Effective Field Theory Approach to the One-Dimensional Scattering Problem

Persistent Link:
http://hdl.handle.net/10150/243871
Title:
An Effective Field Theory Approach to the One-Dimensional Scattering Problem
Author:
Berg, Kevin Michael
Issue Date:
May-2012
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
We 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.
Type:
text; Electronic Thesis
Degree Name:
B.S.
Degree Level:
bachelors
Degree Program:
Honors College; Physics
Degree Grantor:
University of Arizona

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleAn Effective Field Theory Approach to the One-Dimensional Scattering Problemen_US
dc.creatorBerg, Kevin Michaelen_US
dc.contributor.authorBerg, Kevin Michaelen_US
dc.date.issued2012-05-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.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.en_US
dc.typetexten_US
dc.typeElectronic Thesisen_US
thesis.degree.nameB.S.en_US
thesis.degree.levelbachelorsen_US
thesis.degree.disciplineHonors Collegeen_US
thesis.degree.disciplinePhysicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
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