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Theory of Angular Momentum

Wounjhang Park

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,

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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.

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What's inside

Syllabus

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.
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Suitable for graduate students with a background in electrical engineering
The material is quite specific, therefore, suited towards students interested in the topics of angular momentum related to quantum mechanics
The course can be part of the Master of Science in Electrical Engineering degree from CU Boulder, which adds weight to its academic rigor
Utilizes a mix of media, including videos and synchronous discussions
Forms a solid foundation for students to comprehend advanced topics in quantum mechanics

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Reviews summary

Deep dive into quantum angular momentum

According to students, this course provides an incredibly well-structured and rigorous theoretical grounding in angular momentum within quantum mechanics. Learners consistently highlight the instructor's profound understanding and ability to explain complex ideas with clarity. While the course material is dense and demanding, many find it rewarding and essential for advanced studies. Recent reviews suggest that updates to lecture notes and practice problems have further enhanced the learning experience. However, prospective students should be aware of the high prerequisite knowledge required, as the course assumes a strong background in linear algebra and basic quantum mechanics.
Primarily theoretical with fewer practical applications.
"The course delivers exactly what it promises: a deep theoretical understanding... I wished there were more computational examples to solidify the theory."
"The presentation sometimes feels dry, and there's a heavy reliance on just mathematical derivations without much intuitive explanation."
"I found the course quite abstract. While it covers the theory, I struggled to see its direct applications."
"It felt very much like pure academic theory. If you're looking for practical uses of angular momentum, this might not be for you."
Requires strong prior knowledge in related advanced physics.
"I think it's crucial to have a strong foundation in linear algebra and basic quantum mechanics before starting this. Without it, you'll struggle."
"This course is extremely advanced. As someone transitioning from a related field, I found the prerequisites not clearly stated enough. I struggled to keep up."
"Good course for those who are already very strong in quantum mechanics. For me, it was a constant battle."
"The prerequisites are significant; ensure you're comfortable with advanced calculus and linear algebra before enrolling. It's a deep dive."
Course content has been updated and improved over time.
"This course is incredibly well-structured and the instructor's explanations are crystal clear... The recent updates to the lecture notes and practice problems have made it even better."
"The course content is solid, but the delivery could be improved. It feels like a standard university lecture recorded. (Older review, suggesting previous areas for improvement)"
"Came in hoping to learn angular momentum. Left more confused... Needed more interactive elements. (Older review, possibly addressed by recent updates)"
Demanding pace and content, yet highly valuable for learners.
"The pace is demanding, but necessary for the subject matter. The instructor is knowledgeable. I wished there were more computational examples to solidify the theory, but overall, a very good academic course."
"I came into this with a decent physics background, but this course was still quite challenging. The lectures are dense, and sometimes the notation can be overwhelming."
"Well-executed course. The material is dense, but the instructor manages to guide you through it. Definitely enhances one's theoretical physics toolkit."
"A very rigorous course. It dives deep into the mathematical underpinnings. The exercises reinforce the concepts well. It's certainly not for beginners, but highly beneficial."
Instructor's clarity and passion simplify complex quantum concepts.
"This course is incredibly well-structured and the instructor's explanations are crystal clear, especially for such a complex topic."
"A masterclass in quantum angular momentum! The instructor's passion for the subject shines through. The depth of coverage is impressive."
"Outstanding course. The instructor has a profound understanding of the subject and explains it with clarity."
"Absolutely essential for anyone studying quantum mechanics seriously. The instructor’s ability to explain difficult concepts concisely is unparalleled."
Offers a profound and comprehensive theoretical understanding.
"This course is incredibly well-structured and the instructor's explanations are crystal clear, especially for such a complex topic. Highly recommended for anyone serious about quantum mechanics."
"The theoretical grounding is very strong. I personally found some of the initial derivations a bit rushed, but once you get past that, it flows well. A good preparation for advanced topics."
"Fantastic course! The instructor breaks down complex ideas into manageable pieces. I particularly liked the module on general theory of angular momentum; it tied everything together. This course filled significant gaps in my understanding."
"The theoretical rigor of this course is its strongest point. It provides a foundational understanding vital for higher-level physics or engineering."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Theory of Angular Momentum with these activities:
Review angular momentum operators
This activity will help you refresh your understanding of angular momentum operators, which are essential for understanding the behavior of particles with angular momentum.
Show steps
  • Review the definition of angular momentum operators.
  • Practice using angular momentum operators to solve problems.
Watch video tutorials on angular momentum
This activity will help you learn about angular momentum by watching video tutorials.
Browse courses on Angular Momentum
Show steps
  • Find video tutorials on angular momentum.
  • Watch the video tutorials.
  • Take notes on the video tutorials.
Organize your notes on angular momentum
This activity will help you organize your notes on angular momentum, which will make it easier to review and study for exams.
Browse courses on Angular Momentum
Show steps
  • Gather your notes on angular momentum.
  • Organize your notes into a logical order.
  • Create a study guide from your notes.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Study group on angular momentum
This activity will help you learn from and collaborate with other students on the topic of angular momentum.
Browse courses on Angular Momentum
Show steps
  • Find a study group on angular momentum.
  • Attend the study group meetings.
  • Participate in the discussions.
Solve angular momentum problems
This activity will help you practice solving angular momentum problems, which is essential for understanding the behavior of particles with angular momentum.
Browse courses on Quantum Mechanics
Show steps
  • Find practice problems on angular momentum.
  • Solve the practice problems.
  • Check your answers against the solutions.
Write a report on angular momentum
This activity will help you deepen your understanding of angular momentum by writing a report on the topic.
Browse courses on Angular Momentum
Show steps
  • Research angular momentum.
  • Write a report on angular momentum.
  • Submit your report to your instructor.
Create a presentation on angular momentum
This activity will help you deepen your understanding of angular momentum by creating a presentation on the topic.
Browse courses on Angular Momentum
Show steps
  • Research angular momentum.
  • Create a presentation on angular momentum.
  • Present your presentation to others.
Contribute to an open-source project on angular momentum
This activity will help you gain practical experience working with angular momentum concepts.
Browse courses on Angular Momentum
Show steps
  • Find an open-source project on angular momentum.
  • Contribute to the project.
  • Submit your contributions to the project.

Career center

Learners who complete Theory of Angular Momentum will develop knowledge and skills that may be useful to these careers:
Theoretical Physicist
Theoretical physicists develop and test theories about the fundamental nature of the universe. They use their knowledge of mathematics and physics to develop models that explain the behavior of matter and energy. This course on the theory of angular momentum may be useful for theoretical physicists who want to study the fundamental properties of matter and energy.
See salaries and explore the career path for Theoretical Physicist
Research Scientist
Research scientists conduct research in a variety of fields, including physics, chemistry, biology, and engineering. They use their knowledge and skills to develop new products and technologies, and to better understand the world around us. This course on the theory of angular momentum provides a strong foundation for those interested in a research career in physics.
See salaries and explore the career path for Research Scientist
Medical Physicist
Medical physicists use their knowledge of physics to develop and apply techniques for diagnosing and treating diseases. They work with a variety of medical equipment, including radiation therapy machines and magnetic resonance imaging (MRI) machines. This course on theory of angular momentum can be very useful for those that specialize in radiation therapy. The study of commutation relations of angular momentum will be instrumental in understanding the functions of the machines used in radiation therapy.
See salaries and explore the career path for Medical Physicist
Quantum Physicist
Quantum physicists study the behavior of matter and energy at the atomic and subatomic level. They use their knowledge to develop new technologies and to understand the fundamental laws of nature. The section of this course that introduces the quantum mechanical definition of orbital momentum and uses spherical harmonics to express the orbital angular momentum eigenstates may be useful.
See salaries and explore the career path for Quantum Physicist
Physicist
Physicists study the fundamental laws of nature and the physical properties of matter and energy. They use their knowledge to develop new technologies and to understand the universe. This course may be useful to physicists interested in studying the fundamental properties of matter and energy.
See salaries and explore the career path for Physicist
Particle Physicist
Particle physicists study the fundamental building blocks of matter and the forces that act between them. They use a variety of experimental and theoretical techniques to investigate the properties of subatomic particles. The section of this course that introduces the quantum mechanical definition of orbital momentum may be helpful to this field.
See salaries and explore the career path for Particle Physicist
Science Teacher
Science teachers teach science at the elementary, secondary, or post-secondary level. They develop and implement lesson plans, grade assignments, and provide feedback to students. This course on the theory of angular momentum may be useful for science teachers who want to teach physics at the high school or college level.
See salaries and explore the career path for Science Teacher
Spacecraft Engineer
Spacecraft engineers design, build, and test spacecraft. They also work on the development of launch vehicles and ground systems. The section of this course on the theory of angular momentum that discusses the fundamental property of angular momentum and commutation relations among Cartesian components may be useful.
See salaries and explore the career path for Spacecraft Engineer
Astronomer
Astronomers research and study celestial objects like stars, planets, and galaxies. They also study the physical and chemical properties of these objects to better understand the evolution of the universe. This particular course on the theory of angular momentum (specifically the orbital angular momentum), introduces the quantum mechanical definition of orbital momentum. It also uses spherical harmonics to express orbital angular momentum eigenstates and uses them to describe the hydrogen atom. This course may be useful.
See salaries and explore the career path for Astronomer
Nuclear Engineer
Nuclear engineers design, build, and maintain nuclear power plants. They also work on the development of nuclear weapons and other nuclear technologies. The section of this course that discusses the general definition of angular momentum operator based on rotation operator and derives the most fundamental property of angular momentum, commutation relations among their Cartesian components, may be helpful.
See salaries and explore the career path for Nuclear Engineer
Materials Scientist
Materials scientists analyze the structure and properties of materials and develop new materials. In particular, they may work with metals, polymers, and other materials that exhibit different kinds of magnetism. They use their research to develop improvements in existing materials and to develop entirely new materials for use in a variety of industries. The section of this course that introduces the general definition of angular momentum operator based on rotation operator, and discusses the properties of spin-1/2 systems (like electrons) may be helpful.
See salaries and explore the career path for Materials Scientist
Plasma Physicist
Plasma physicists study the behavior of plasma, which is a state of matter that is composed of ionized gas. Plasma is found in a variety of astrophysical and industrial applications. The section of this course that introduces the general definition of angular momentum operator based on rotation operator, and discusses the properties of spin-1/2 systems, may be helpful.
See salaries and explore the career path for Plasma Physicist
Nanoscientist
Nanoscientists study the properties of materials and devices at the atomic and molecular level. Much of their work is in the field of physics, and their research has applications in a variety of fields, including medicine, manufacturing, and energy. The section of this course that introduces the general definition of angular momentum operator based on rotation operator, and discusses the properties of spin-1/2 systems may be helpful.
See salaries and explore the career path for Nanoscientist
Meteorologist
Meteorologists study the atmosphere and its behavior, including weather patterns and climate change. They use their knowledge to forecast the weather, issue weather warnings and advisories, and conduct research on atmospheric phenomena. The section of this course that discusses the fundamental property of angular momentum, commutation relations among their Cartesian components, may be useful.
See salaries and explore the career path for Meteorologist
Optometrist
Optometrists provide eye care, including vision testing, diagnosis, and treatment of eye diseases. They also prescribe and fit corrective lenses. The section of this course that covers the commutation relations of angular momentum and defines angular momentum eigenstates may be helpful in developing treatments for eye diseases.
See salaries and explore the career path for Optometrist

Reading list

We've selected ten books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Theory of Angular Momentum.
Cover image
Socio-Political Reflections and Civil Defense
Save
This classic text provides a detailed treatment of the theory of groups and quantum mechanics, including the role of angular momentum.
Socio-Political Reflections and Civil Defense (The...
Hardcover
$$$$
Socio-Political Reflections and Civil Defense...
Paperback
$$$$
Cover image
Introduction to Electrodynamics
Save
Provides a comprehensive overview of quantum mechanics, including the theory of angular momentum.
Introduction to Electrodynamics
Hardcover
$$$
Introduction to Electrodynamics
Paperback
$$$
INTRODUCTION TO ELECTRODYNAMICS, 4TH EDITION
Paperback
$$
Introduction to Electrodynamics
Hardcover
$$$
Introduction to Electrodynamics
Kindle Edition
$$$
Introduction to Electrodynamics
Kindle Edition
$$$
Cover image
Quantum Theory Of Angular Momemtum
Save
Provides a comprehensive overview of the quantum theory of angular momentum.
Quantum Theory of Angular Momemtum
Paperback
$$$
Cover image
Angular Momentum in Quantum Mechanics
Save
Provides a comprehensive overview of angular momentum in quantum physics.
Angular Momentum in Quantum Mechanics...
Paperback
$$
Angular Momentum in Quantum Mechanics...
Kindle Edition
$$
Cover image
The Racah-Wigner Algebra in Quantum Theory
Save
This advanced textbook covers the theory of angular momentum in great detail.
The Racah-Wigner Algebra in Quantum Theory...
Paperback
$$$$
Cover image
Selected Scientific Papers of E.U. Condon
Save
This classic text provides a detailed treatment of the theory of atomic spectra, including the role of angular momentum.
Selected Scientific Papers of E.U. Condon
Paperback
$$$
Cover image
Spectroscopic Measurement
Save
Provides a comprehensive overview of quantum mechanics, including the theory of angular momentum.
Spectroscopic Measurement: An Introduction to the...
Kindle Edition
$$$$
Spectroscopic Measurement: An Introduction to the...
Kindle Edition
$$$$
Cover image
Quantum Mechanics: A Modern Development (2nd...
Save
Provides a comprehensive overview of quantum mechanics, including the theory of angular momentum.
QUANTUM MECHANICS: A MODERN DEVELOPMENT (2ND...
Hardcover
$$$$
Quantum Mechanics: A Modern Development (2nd...
Kindle Edition
$$
Cover image
Fundamentals of Molecular Symmetry
Save
Provides a comprehensive overview of molecular symmetry and spectroscopy, including the role of angular momentum.
Fundamentals of Molecular Symmetry (Series in...
Paperback
$$$
Principles of Quantum Mechanics
Save
Provides a clear and concise introduction to quantum mechanics, including the theory of angular momentum.
Principles of Quantum Mechanics
Paperback
Check
Principles of Quantum Mechanics
Kindle Edition
Check

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Effort
Approx. 12 hours
Level
Intermediate
Via
Coursera
Institution
University of Colorado Boulder
Instructor
Wounjhang Park
Language
English
Transcripts
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This course belongs to a collection called Quantum Mechanics for Engineers. It's comprised of three courses:
  1. Theory of Angular Momentum (viewing)
  2. Foundations of Quantum Mechanics
  3. Approximation Methods
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Suitable for graduate students with a background in electrical engineering
The material is quite specific, therefore, suited towards students interested in the topics of angular momentum related to quantum mechanics
The course can be part of the Master of Science in Electrical Engineering degree from CU Boulder, which adds weight to its academic rigor
Utilizes a mix of media, including videos and synchronous discussions
Forms a solid foundation for students to comprehend advanced topics in quantum mechanics
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