This course can also be taken for academic credit as ECEA xxxx, part of CU Boulder’s Master of Science in Electrical Engineering degree. 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.
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At the end of this course learners will be able to:
- describe and analyze angular momentum states using quantum mechanically defined angular momentum operators,
- solve angular momentum eigenvalue equations and
- add angular momenta quantum mechanically.
What You Will Learn
- Specify the quantum states of the electron in a hydrogen atom.
- Describe spin states quantum mechanically.
- Solve eigenvalue equations of angular momentum operators.
- Add general angular momenta.
Course 2 of 3 in the Quantum Mechanics for Engineers Specialization
Syllabus
WEEK 1
Orbital Angular Momentum and Hydrogen Atom
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.
WEEK 2
Rotation and Angular Momentum
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.
WEEK 3
General Theory of Angular Momentum
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.
