Discrete variable representation of the angular variables in quantum three-body scattering

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).