Award Date

12-1-2012

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Physics and Astronomy

First Committee Member

Bernard Zygelman

Second Committee Member

Tao Pang

Third Committee Member

Michael Pravica

Fourth Committee Member

Kathleen Robins

Number of Pages

73

Abstract

The Born-Oppenheimer approximation has long been the standard approach to solving the Schrödinger equation for diatomic molecules. In it, nuclear and electronic motions are separated into "slow" and "fast" degrees of freedom and couplings between the two are ignored. The neglect of non-adiabatic couplings leads to an incomplete description of diatomic motion, and in a more refined approach, non-adiabatic couplings are uncoupled by transforming the angular momentum of the molecule and electrons into the body-fixed frame.

In this thesis we examine a "modern" form of the Born-Oppenheimer approximation by exploiting a gauge theoretic approach in a description of molecular motion. This procedure is described by a U(1) gauge field theory which we call the gauge covariant Born-Oppenheimer approximation. Using this approach we show that the non-adiabatic coupling terms are reproduced and manifest as an effective magnetic monopole vector potential that gives rise to an effective Lorentz type force.

Keywords

Adiabatic; Born-Oppenheimer approximation; Degree of freedom; Diatomic molecules; Energy transfer; Gauge theory; Magnetic monopoles; Molecular Hamiltonian; Quantum theory

Disciplines

Atomic, Molecular and Optical Physics | Quantum Physics

Language

English


Share

COinS