ECEA 5612 Approximation Methods
3rd course in the Quantum Mechanics for Engineers Specialization
Instructor: Wounjhang Park,ÌýPh.D., Professor
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.
Prior knowledge needed:ÌýIntroductory physics including electromagnetics and modern physics and Introductory calculus and ordinary differential equations
Learning Outcomes
- Use time-dependent perturbation theory to obtain first- and second -order corrections to energies and wavefunctions
- Use time-dependent perturbation theory and obtain transition rates
- Use tight binding method, variational method and finite basis set to obtain approximate solutions of various quantum mechanics problems.
Syllabus
Duration: 5.5Ìýhours
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. ÌýWe will also discuss specific examples where the various perturbation methods are used - Stark effect, fine structure and Zeeman effect.
Duration: 5Ìýhours
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.
Duration: 4Ìýhours
This module covers several non-perturbative approximation methods. They are the tight binding method, variational method and the use of finite basis set.
Duration: 3.5Ìýhours
Final exam for the course.
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Grading
Assignment | Percentage of Grade |
|---|---|
Homework #1 | 18% |
Peer Review: Rabi Oscillation | 6% |
Homework #2 | 18% |
Homework #3 | 18% |
Final Exam | 40% |
Letter Grade Rubric
Letter GradeÌý | Minimum Percentage |
|---|---|
A | 95% |
A- | 90% |
B+ | 85% |
B | 80% |
B- | 75% |
C+ | 70% |
C | 65% |
C- | 60% |
D+ | 55% |
D | 50% |
F | 0% |