Approximation Methods

Overview

Class Central Tips

This course can also be taken for academic credit as ECEA 5612, part of CU Boulder’s Master of Science in Electrical Engineering degree. This course teaches commonly used approximation methods in quantum mechanics. They include time-independent perturbation theory, time-dependent perturbation theory, tight binding method, variational method and the use of finite basis set. In each case, a specific example is given to clearly show how the method works. At the end of this course learners will be able to: 1. use time-dependent perturbation theory to obtain first- and second -order corrections to energies and wavefunctions, 2. use time-dependent perturbation theory and obtain transition rates, and 3. use tight binding method, variational method and finite basis set to obtain approximate solutions of various quantum mechanics problems.

Syllabus

Time-independent Perturbation Theory

In this module we will introduce the course on approximation methods commonly used in quantum mechanics and then discuss time-independent perturbation theory. We will first discuss non-degenerate perturbation theory and derive useful formulas for the first- and second-order corrections. We will then discuss degenerate perturbation theory. We will also discuss specific examples where the various perturbation methods are used - Stark effect, fine structure and Zeeman effect.

Time-dependent Perturbation Theory

In this module, we will introduce interaction picture and derive time evolution equations. After discussing a simple but illuminating example of two-state system, we develop time-dependent perturbation theory and discuss the probability of transitions between quantum states induced by external perturbation.

Other Approximation Methods

This module covers several non-perturbative approximation methods. They are the tight binding method, variational method and the use of finite basis set.