3rd course in the Quantum Mechanics for Engineers Specialization

Instructor: Wounjhang Park, Ph.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: Introductory 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: 5.5 hours

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.

Duration: 5 hours

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: 4 hours

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

Duration: 3.5 hours

Final exam for the course.

##### Assignment

Homework #1

18%

Peer Review: Rabi Oscillation

6%

Homework #2

18%

Homework #3

18%

Final Exam

40%

A

95%

A-

90%

B+

85%

B

80%

B-

75%

C+

70%

C

65%

C-

60%

D+

55%

D

50%

F

0%