2nd course in the Quantum Mechanics for Engineers Specialization

Instructor: Wounjhang Park, Ph.D., Professor

This course introduces the quantum mechanical concept of angular momentum operator and its relationship with rotation operator. It then presents the angular momentum operators, their eigenvalues and eigenfunctions. Finally, it covers the theory of angular momentum addition.

Prior knowledge needed: Introductory physics including electromagnetics and modern physics and Introductory calculus and ordinary differential equations

### Learning Outcomes

• Describe and analyze angular momentum states using quantum mechanically defined angular momentum operators
• Solve angular momentum eigenvalue equations
• Add angular momenta quantum mechanically

### Syllabus

Duration: 4 hours

In this module we will introduce the course on the theory of angular momentum and then introduce the quantum mechanical definition of orbital  momentum. We will then use the spherical harmonics to express the orbital angular momentum eigenstates and use them to describe the hydrogen atom states.

Duration: 3.5 hours

In this module, we introduce the general definition of angular momentum operator based on rotation operator. This general definition allows both orbital and spin angular momentum. We then derive the most fundamental property of angular momentum - commutation relations among their Cartesian components. Finally, we discuss the properties of spin-1/2 system.

Duration: 5.5 hours

This module covers the general theory of angular momentum. We start with the commutation relation of angular momentum and define angular momentum eigenstates. We then construct matrix representation of rotation operators using the angular momentum eigenstates as the basis set. Finally, we discuss how to quantum mechanically add angular momenta.

Duration: 3.5 hours

Final exam for the course.

##### Percentage of Grade

Homework #1

18%

Homework #2

18%

Peer Review: Angular Momentum Addition

6%

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%