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Theory of Angular Momentum

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Theory of Angular Momentum

This course is part of Quantum Mechanics for Engineers Specialization

Instructor: Wounjhang Park

6,316 already enrolled

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3 modules

Gain insight into a topic and learn the fundamentals.

20 reviews

Intermediate level

Recommended experience

Flexible schedule

1 week at 10 hours a week

Learn at your own pace

Build toward a degree

Learn more

3 modules

Gain insight into a topic and learn the fundamentals.

20 reviews

Intermediate level

Recommended experience

Flexible schedule

1 week at 10 hours a week

Learn at your own pace

Build toward a degree

Learn more

What you'll 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'll gain

Details to know

Shareable certificate

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Assessments

3 assignments

Taught in English

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This course is part of the Quantum Mechanics for Engineers Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 3 modules in this course

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.

Module details

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.

What's included

5 videos6 readings1 assignment2 discussion prompts

5 videosTotal 56 minutes

Course Introduction2 minutes
Orbital Angular Momentum 19 minutes
Orbital Angular Momentum 211 minutes
Hydrogen Atom 113 minutes
Hydrogen Atom 221 minutes

6 readingsTotal 42 minutes

Course Updates and Accessibility Support1 minute
Non-Credit Students: Welcome and Where to Find Help10 minutes
Suggested textbooks10 minutes
Module Topics1 minute
Physical Constants10 minutes
Entering Math Expressions10 minutes

1 assignmentTotal 120 minutes

Homework #1120 minutes

2 discussion promptsTotal 20 minutes

Introduce Yourself10 minutes
Spherical Harmonics10 minutes

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.

What's included

4 videos3 readings1 assignment1 discussion prompt

4 videosTotal 58 minutes

Rotation Operator17 minutes
Properties of Rotation Operator11 minutes
Rotation of Spin 1/2 System16 minutes
Spinor13 minutes

3 readingsTotal 21 minutes

Module Topics1 minute
Physical Constants10 minutes
Entering Math Expressions10 minutes

1 assignmentTotal 120 minutes

Homework #2120 minutes

1 discussion promptTotal 10 minutes

Rotation of Spin State10 minutes

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.

What's included

6 videos3 readings1 assignment1 peer review

6 videosTotal 112 minutes

General Definition of Angular Momentum15 minutes
Rotation Matrices21 minutes
Matrix Representation of Angular Momentum Operators15 minutes
Orbital Angular Momentum Revisited23 minutes
Addition of Angular Momentum22 minutes
General Theory of Angular Momentum Addition16 minutes

3 readingsTotal 30 minutes

Module Topics10 minutes
Physical Constants10 minutes
Entering Math Expressions10 minutes

1 assignmentTotal 120 minutes

Homework #3120 minutes

1 peer reviewTotal 60 minutes

Angular Momentum Addition60 minutes

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Build toward a degree

This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹