This course can also be taken for academic credit as ECEA 5611, part of CU Boulder’s Master of Science in Electrical Engineering degree.
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About this Course
Undergraduate-level calculus, differential equations and linear algebra
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.
Skills you will gain
- angular momentum
- Quantum Mechanics
- hydrogen atom
Undergraduate-level calculus, differential equations and linear algebra
Offered by

University of Colorado Boulder
CU-Boulder is a dynamic community of scholars and learners on one of the most spectacular college campuses in the country. As one of 34 U.S. public institutions in the prestigious Association of American Universities (AAU), we have a proud tradition of academic excellence, with five Nobel laureates and more than 50 members of prestigious academic academies.
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Syllabus - What you will learn from this course
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.
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.
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.
About the Quantum Mechanics for Engineers Specialization
This Specialization is intended for engineers seeking to acquire fundamental understanding of quantum mechanics which are the basis of modern electrical, mechanical and quantum engineering. Through 3 courses, you will learn (1) basic concepts such as superposition and entanglement of quantum states, measurement in quantum mechanics and uncertainty principle, (2) mathematical tools needed to describe and manipulate quantum states, (3) advanced theory of angular momentum and (4) approximation methods widely applicable in many fields.

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