Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering

<p>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).</p>

Name thesis:degree_name

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

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

School of Mathematical Sciences

Year dc:date.available

2011

Author dc:creator

• Caballero, David

Contributors dc:contributor

• C.Y. Hu
• Ellis Cumberbatch
• Ali Nadim

• Mathematics
• Physics

Repository record dc:identifier

https://scholarship.claremont.edu/cgu_etd/11

OAI identifier oai:identifier

oai:scholarship.claremont.edu:cgu_etd-1014