Usual and Unusual Perturbative expansion parameters in Quantum Mechanics
Introduction
This project was undertaken during the 2022/2023 academic year. It was the Senior Honours project for my MPhys degree in Theoretical Physics at the University of Edinburgh. The project was done under the supervision of Dr Sašo Grozdanov.
Abstract
This report briefly introduces perturbation theory and discusses the divergence of perturbation series and how to deal with it using Padé Summation. Then it explores the 1/N expansion method in Quantum mechanics. In particular, two different methods to obtain the coefficients of this expansion are explained using the Hydrogen atom as an example. This method is then validated by looking at the results that it provides for different physical systems and comparing them with literature values. Finally, the 1/N expansion is used to analyse the energy levels of the Yukawa potential in great detail.