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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.
Read more
This course can also be taken for academic credit as ECEA 5611, part of CU Boulder’s Master of Science in Electrical Engineering degree.
Read more
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.
Register for this course and see more details by visiting:
OpenCourser.com/course/3dasxx/theory
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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.
Read more
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.
Read more
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.
Good to know
Good to know
Know what's good ,
what to watch for , 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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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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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
Show steps
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.
Review angular momentum operators
Show steps
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
Show steps
Show steps
- Review the definition of angular momentum operators.
- Practice using angular momentum operators to solve problems.
Watch video tutorials on angular momentum
Show steps
This activity will help you learn about angular momentum by watching video tutorials.
Browse courses on
Angular Momentum
Show steps
Show steps
Show steps
- Find video tutorials on angular momentum.
- Watch the video tutorials.
- Take notes on the video tutorials.
Organize your notes on angular momentum
Show steps
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
Show steps
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
Show steps
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
Show steps
Show steps
- Find a study group on angular momentum.
- Attend the study group meetings.
- Participate in the discussions.
Solve angular momentum problems
Show steps
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
Show steps
Show steps
- Find practice problems on angular momentum.
- Solve the practice problems.
- Check your answers against the solutions.
Write a report on angular momentum
Show steps
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
Show steps
Show steps
- Research angular momentum.
- Write a report on angular momentum.
- Submit your report to your instructor.
Create a presentation on angular momentum
Show steps
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
Show steps
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
Show steps
This activity will help you gain practical experience working with angular momentum concepts.
Browse courses on
Angular Momentum
Show steps
Show steps
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 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.
Research Scientist
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.
Medical Physicist
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.
Quantum 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.
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.
Particle 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.
Science Teacher
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.
Spacecraft Engineer
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.
Astronomer
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.
Nuclear Engineer
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.
Materials Scientist
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.
Plasma Physicist
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.
Nanoscientist
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.
Meteorologist
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.
Optometrist
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.
For more career information including salaries, visit:
OpenCourser.com/course/3dasxx/theory
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.
This classic text provides a detailed treatment of the theory of groups and quantum mechanics, including the role of angular momentum.
Provides a comprehensive overview of quantum mechanics, including the theory of angular momentum.
Provides a comprehensive overview of the quantum theory of angular momentum.
Provides a comprehensive overview of angular momentum in quantum physics.
This advanced textbook covers the theory of angular momentum in great detail.
This classic text provides a detailed treatment of the theory of atomic spectra, including the role of angular momentum.
Provides a comprehensive overview of quantum mechanics, including the theory of angular momentum.
Provides a comprehensive overview of quantum mechanics, including the theory of angular momentum.
Provides a comprehensive overview of molecular symmetry and spectroscopy, including the role of angular momentum.
Provides a clear and concise introduction to quantum mechanics, including the theory of angular momentum.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/3dasxx/theory
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Effort
Consists of 3 Modules, between 2 and 5 hours of work per module.
Level
Intermediate
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Institution
University of Colorado Boulder
Instructor
Wounjhang Park
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English
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This course belongs to a
collection
called
Quantum Mechanics for Engineers. It's comprised of three courses:
- Theory of Angular Momentum (viewing)
- Approximation Methods
- Foundations of Quantum Mechanics
Good to know
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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