This course is part of the Quantum Mechanics for Engineers Specialization

Wounjhang Park

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Part of the Master of Science in Electrical Engineering degree

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Quantum Mechanics for Engineers SpecializationUniversity of Colorado Boulder

About this Course

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This course can also be taken for academic credit as ECEA 5611, 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. 

At the end of this course learners will be able to:
1. describe and analyze angular momentum states using quantum mechanically defined angular momentum operators,
2. solve angular momentum eigenvalue equations and
3. add angular momenta quantum mechanically.

Flexible deadlines

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Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 2 of 3 in the

Quantum Mechanics for Engineers Specialization

Intermediate Level

Undergraduate-level calculus, differential equations and linear algebra

Approx. 13 hours to complete

English

Subtitles: English

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

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 2 of 3 in the

Quantum Mechanics for Engineers Specialization

Intermediate Level

Undergraduate-level calculus, differential equations and linear algebra

Approx. 13 hours to complete

English

Subtitles: English

Instructor

Wounjhang Park

Professor

Electrical, Computer, and Energy Engineering

31,783 Learners

6 Courses

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.

Start working towards your Master's degree

This course is part of the 100% online Master of Science in Electrical Engineering from University of Colorado Boulder. If you are admitted to the full program, your courses count towards your degree learning.

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Syllabus - What you will learn from this course

Week

Week 1

4 hours to complete

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.

4 hours to complete

5 videos (Total 56 min), 4 readings, 1 quiz

Week

Week 2

3 hours to complete

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.

3 hours to complete

4 videos (Total 58 min), 3 readings, 1 quiz

Week

Week 3

5 hours to complete

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.

5 hours to complete

6 videos (Total 112 min), 3 readings, 2 quizzes

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.

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

More questions? Visit the Learner Help Center.

Theory of Angular Momentum