ECEA 5611 Theory of Angular Momentum
2nd course in the Quantum Mechanics for Engineers Specialization
Instructor: Wounjhang Park,ÌýPh.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:ÌýIntroductory 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: 4Ìýhours
In this module we will introduce the course on the theory of angular momentum and then introduce the quantum mechanical definition of orbital Ìýmomentum. 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: 5.5Ìýhours
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: 3.5Ìýhours
Final exam for the course.
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Grading
Assignment | Percentage of Grade |
---|---|
Homework #1 | 18% |
Homework #2 | 18% |
Peer Review: Angular Momentum Addition | 6% |
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% |