Date of Award

Winter 2011

Degree Type

Open Access Dissertation

Degree Name

Engineering and Industrial Applied Mathematics Joint PhD with California State University Long Beach, PhD

Program

School of Mathematical Sciences

Advisor/Supervisor/Committee Chair

Alfonso Rueda

Dissertation or Thesis Committee Member

C.Y. Hu

Dissertation or Thesis Committee Member

Ellis Cumberbatch

Dissertation or Thesis Committee Member

Ali Nadim

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2011 David Caballero

Abstract

There are many numerical methods to study the quantum mechanical three-body scattering system using the Schrodinger equation. Traditionally, a partial-wave decomposition of the total wave function is carried out first, allowing the scattering system to be solved one partial wave at a time. This is convenient when the interaction is central, causing the total angular momentum to be conserved during the collision process. This is not possible in the presence of a non-central interaction such as a laser field, where the total angular momentum is not conserved during the collision process. The Discrete Variable Representation is a new method for solving the quantum-mechanical three-body scattering problem to obtain the total cross section. The implementation of this new method for the two-body problem has been successfully applied to real systems. The extension to the three-body problem is the next logical step. For this thesis bipolar spherical harmonics are used in the implementation of the three-body Discrete Variable Representation. This Discrete Variable Representation is capable of working with any combination of interactions, including non-central interactions. The total cross section computation for a three-particle elastic-scattering numerical example is used to illustrate the potential of this Discrete Variable Representation method. The three-particle system consists of a positron scattering against a ground state hydrogen atom (an electron bound to a proton).

DOI

10.5642/cguetd/11

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