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).
","abstract_html":"<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>","abstract_has_math":false,"creators":["Caballero, David"],"institution":null,"degree_name":"Engineering and Industrial Applied Mathematics Joint PhD with California State University Long Beach, PhD","degree_level":"Open Access Dissertation","degree_discipline":"School of Mathematical Sciences","degree_department":null,"school":null,"contributors":["C.Y. Hu","Ellis Cumberbatch","Ali Nadim"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T01:39:44Z","subjects":["Mathematics","Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarship.claremont.edu/cgu_etd/11","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["C.Y. Hu","Ellis Cumberbatch","Ali Nadim"]},{"key":"dc:creator","label":"Author","values":["Caballero, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2012-02-08T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["School of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Engineering and Industrial Applied Mathematics Joint PhD with California State University Long Beach, PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarship.claremont.edu/cgu_etd/11"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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).
"]},{"key":"dc:title","label":"Title","values":["Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering"]}]}],"canonical_facts":{"dc:contributor":["C.Y. Hu","Ellis Cumberbatch","Ali Nadim"],"dc:creator":["Caballero, David"],"dc:date.available":["2012-02-08T08:00:00Z"],"dc:description.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).
"],"dc:identifier":["https://scholarship.claremont.edu/cgu_etd/11"],"dc:subject":["Mathematics","Physics"],"dc:title":["Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering"],"thesis:degree_discipline":["School of Mathematical Sciences"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Engineering and Industrial Applied Mathematics Joint PhD with California State University Long Beach, PhD"]},"updated_at":"2026-07-24T01:39:44Z"}