Date of Award

Spring 5-22-2017

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Physics

First Advisor

Xiao-Qian Wang, Ph.D.

Second Advisor

Ronald E. Mickens, Ph.D.

Third Advisor

Alfred A. Msezane, Ph.D.

Abstract

Numerical solutions of quantum mechanical problems have witnessed tremendous advances over the past years. In this thesis, we develop an iterative approach to problems of double-well potentials and their variants with parity-time-reversal symmetry- breaking perturbations. We show that the method provides an efficient scheme for obtaining accurate energies and wave functions. We discuss in this thesis potential applications to a variety of related topics such as phase transitions, symmetry breaking, and external field-induced effects.

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