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Wounjhang Park
This course can also be taken for academic credit as ECEA 5612, 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 5612, 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 5612, part of CU Boulder’s Master of Science in Electrical Engineering degree.
This course teaches commonly used approximation methods in quantum mechanics. They include time-independent perturbation theory, time-dependent perturbation theory, tight binding method, variational method and the use of finite basis set. In each case, a specific example is given to clearly show how the method works.
At the end of this course learners will be able to:
1. use time-dependent perturbation theory to obtain first- and second -order corrections to energies and wavefunctions,
2. use time-dependent perturbation theory and obtain transition rates, and
3. use tight binding method, variational method and finite basis set to obtain approximate solutions of various quantum mechanics problems.
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What's inside
Syllabus
Time-independent Perturbation Theory
In this module we will introduce the course on approximation methods commonly used in quantum mechanics and then discuss time-independent perturbation theory. We will first discuss non-degenerate perturbation theory and derive useful formulas for the first- and second-order corrections. We will then discuss degenerate perturbation theory. We will also discuss specific examples where the various perturbation methods are used - Stark effect, fine structure and Zeeman effect.
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Syllabus
Time-independent Perturbation Theory
In this module we will introduce the course on approximation methods commonly used in quantum mechanics and then discuss time-independent perturbation theory. We will first discuss non-degenerate perturbation theory and derive useful formulas for the first- and second-order corrections. We will then discuss degenerate perturbation theory. We will also discuss specific examples where the various perturbation methods are used - Stark effect, fine structure and Zeeman effect.
Read more
Time-dependent Perturbation Theory
In this module, we will introduce interaction picture and derive time evolution equations. After discussing a simple but illuminating example of two-state system, we develop time-dependent perturbation theory and discuss the probability of transitions between quantum states induced by external perturbation.
Other Approximation Methods
This module covers several non-perturbative approximation methods. They are the tight binding method, variational method and the use of finite basis set.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Suitable for individuals with a basic background in quantum mechanics who seek to enhance their understanding of approximation methods
Provides practical examples to demonstrate the effective application of each method
Enhances problem-solving capabilities by equipping learners to tackle various quantum mechanics issues using appropriate techniques
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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 Approximation Methods with these
activities:
Explore Online Perturbation Theory Tutorials
Show steps
Watching tutorials can provide additional insights and explanations.
Browse courses on
Quantum Mechanics
Show steps
-
Search for online tutorials on perturbation theory.
-
Choose a tutorial that aligns with your learning style.
-
Follow the tutorial and take notes.
Solve Sample Problems
Show steps
Practice solving perturbation theory problems to deepen your understanding of the concepts.
Browse courses on
Quantum Mechanics
Show steps
-
Identify the perturbation and unperturbed system.
-
Apply the appropriate perturbation theory method.
-
Calculate the corrections to the energy and wavefunction.
Attend Virtual Study Groups
Show steps
Discussing the material with peers can help you identify and address misunderstandings.
Browse courses on
Quantum Mechanics
Show steps
-
Find or create a virtual study group.
-
Prepare questions and discussion points in advance.
-
Actively participate in the discussion.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Write a Summary of Key Concepts
Show steps
Summarizing the key concepts will help you organize and solidify your understanding.
Browse courses on
Quantum Mechanics
Show steps
-
Identify the most important concepts in each module.
-
Write a concise and clear summary of each concept.
-
Review and revise your summary regularly.
Read Selected Chapters from Shankar's Principles of Quantum Mechanics
Show steps
Shankar's book provides a comprehensive and in-depth treatment of perturbation theory.
View
Principles of Quantum Mechanics
on Amazon
Show steps
-
Identify the relevant chapters on perturbation theory.
-
Read the chapters carefully and take notes.
-
Solve the practice problems at the end of each chapter.
Develop a MATLAB Script for Perturbation Calculations
Show steps
Creating a MATLAB script will allow you to apply your knowledge to practical problems.
Browse courses on
Quantum Mechanics
Show steps
-
Learn the basics of MATLAB programming.
-
Identify a specific perturbation problem to solve.
-
Write a MATLAB script to implement the perturbation theory method.
-
Test and debug your script.
Attend a Workshop on Perturbation Theory Applications
Show steps
Workshops provide an opportunity to learn from experts and engage in hands-on activities.
Browse courses on
Quantum Mechanics
Show steps
-
Identify workshops related to perturbation theory.
-
Register for a relevant workshop.
-
Attend the workshop and actively participate.
Contribute to Open-Source Projects in Quantum Physics
Show steps
Contributing to open-source projects will provide practical experience and help build your knowledge.
Browse courses on
Quantum Mechanics
Show steps
-
Identify open-source projects related to quantum perturbation theory.
-
Read the project documentation and familiarize yourself with the codebase.
-
Identify areas where you can contribute your skills.
Explore Online Perturbation Theory Tutorials
Show steps
Watching tutorials can provide additional insights and explanations.
Browse courses on
Quantum Mechanics
Show steps
Show steps
Show steps
- Search for online tutorials on perturbation theory.
- Choose a tutorial that aligns with your learning style.
- Follow the tutorial and take notes.
Solve Sample Problems
Show steps
Practice solving perturbation theory problems to deepen your understanding of the concepts.
Browse courses on
Quantum Mechanics
Show steps
Show steps
Show steps
- Identify the perturbation and unperturbed system.
- Apply the appropriate perturbation theory method.
- Calculate the corrections to the energy and wavefunction.
Attend Virtual Study Groups
Show steps
Discussing the material with peers can help you identify and address misunderstandings.
Browse courses on
Quantum Mechanics
Show steps
Show steps
Show steps
- Find or create a virtual study group.
- Prepare questions and discussion points in advance.
- Actively participate in the discussion.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Write a Summary of Key Concepts
Show steps
Summarizing the key concepts will help you organize and solidify your understanding.
Browse courses on
Quantum Mechanics
Show steps
Show steps
Show steps
- Identify the most important concepts in each module.
- Write a concise and clear summary of each concept.
- Review and revise your summary regularly.
Read Selected Chapters from Shankar's Principles of Quantum Mechanics
Show steps
Shankar's book provides a comprehensive and in-depth treatment of perturbation theory.
View
Principles of Quantum Mechanics
on Amazon
Show steps
Show steps
Show steps
- Identify the relevant chapters on perturbation theory.
- Read the chapters carefully and take notes.
- Solve the practice problems at the end of each chapter.
Develop a MATLAB Script for Perturbation Calculations
Show steps
Creating a MATLAB script will allow you to apply your knowledge to practical problems.
Browse courses on
Quantum Mechanics
Show steps
Show steps
Show steps
- Learn the basics of MATLAB programming.
- Identify a specific perturbation problem to solve.
- Write a MATLAB script to implement the perturbation theory method.
- Test and debug your script.
Attend a Workshop on Perturbation Theory Applications
Show steps
Workshops provide an opportunity to learn from experts and engage in hands-on activities.
Browse courses on
Quantum Mechanics
Show steps
Show steps
Show steps
- Identify workshops related to perturbation theory.
- Register for a relevant workshop.
- Attend the workshop and actively participate.
Contribute to Open-Source Projects in Quantum Physics
Show steps
Contributing to open-source projects will provide practical experience and help build your knowledge.
Browse courses on
Quantum Mechanics
Show steps
Show steps
Show steps
- Identify open-source projects related to quantum perturbation theory.
- Read the project documentation and familiarize yourself with the codebase.
- Identify areas where you can contribute your skills.
Career center
Learners who complete Approximation Methods will develop knowledge and skills
that may be useful to these careers:
Quantum Physicist
Quantum Physicist
Quantum Physicists work on the fundamental nature of energy and matter at the atomic and subatomic levels. Courses in quantum mechanics can help build a foundation in quantum theory, including areas like time-independent perturbation theory, time-dependent perturbation theory, and the variational method. A course such as Approximation Methods can provide exposure to these topics and more, assisting Quantum Physicists in advancing their understanding of quantum systems.
Quantum Programmer
Quantum Programmer
Quantum Programmers write and maintain software for quantum computers. Knowledge of quantum mechanics is essential for this role. A course such as Approximation Methods, which covers topics like time-independent perturbation theory, time-dependent perturbation theory, and the variational method, can provide a strong foundation in quantum theory and prepare individuals for a career as a Quantum Programmer.
Quantum Computing Software Developer
Quantum Computing Software Developer
Quantum Software Developers are responsible for the design and creation of software for quantum systems. A strong background in quantum mechanics is essential for this profession, as the software often involves developing ways to operate quantum computers and solve complex problems. A course such as Approximation Methods covers topics like time-independent perturbation theory, time-dependent perturbation theory, and the variational method, which are fundamental concepts in quantum mechanics. By understanding these principles, Quantum Software Developers can gain a better grasp of how quantum computers work and how to develop effective software for them.
Quantum Software Engineer
Quantum Software Engineer
Quantum Software Engineers design and develop software for quantum computers. Knowledge of quantum mechanics is essential for this role. A course such as Approximation Methods, which covers topics like time-independent perturbation theory, time-dependent perturbation theory, and the variational method, can provide a strong foundation in quantum theory and prepare individuals for a career as a Quantum Software Engineer.
Quantum Algorithm Developer
Quantum Algorithm Developer
Quantum Algorithm Developers design and develop algorithms for quantum computers. Knowledge of quantum mechanics is essential for this role. A course such as Approximation Methods, which covers topics like time-independent perturbation theory, time-dependent perturbation theory, and the variational method, can provide a strong foundation in quantum theory and prepare individuals for a career as a Quantum Algorithm Developer.
Quantum Computing Scientist
Quantum Computing Scientist
Quantum Computing Scientists work on the development of quantum computers and related technologies. Courses in quantum mechanics can help build a foundation in quantum theory, including areas like time-independent perturbation theory, time-dependent perturbation theory, and the variational method. A course such as Approximation Methods can provide exposure to these topics and more, assisting Quantum Computing Scientists in advancing their understanding of quantum systems.
Theoretical Physicist
Theoretical Physicist
Theoretical Physicists develop theories explaining the physical universe. One area of study for Theoretical Physicists is quantum mechanics. Courses in the subject can help build a foundation in quantum theory, including areas like time-independent perturbation theory, time-dependent perturbation theory, and the variational method. A course such as Approximation Methods can provide exposure to these topics and more, assisting Theoretical Physicists in advancing their understanding of quantum systems.
Optoelectronics Engineer
Optoelectronics Engineer
Optoelectronics Engineers research, design, develop, and test optoelectronic devices and systems, including lasers, LEDs, and fiber optic networks. Many of these devices rely on principles of quantum mechanics for their operation. A course such as Approximation Methods can provide exposure to these topics, assisting Optoelectronics Engineers in expanding their knowledge of quantum mechanics and its applications in this field.
Professor
Professor
Professors teach and conduct research in their field of expertise at colleges and universities and often hold doctorates in their field. Many are responsible for teaching a range of advanced courses in quantum mechanics. A course such as Approximation Methods can provide exposure to topics such as time-independent perturbation theory, time-dependent perturbation theory, and the variational method, assisting Professors in expanding their knowledge of quantum mechanics for teaching.
Quantum Information Scientist
Quantum Information Scientist
Quantum Information Scientists research and develop ways to use quantum mechanics to process and transmit information. Courses in the subject can help build a foundation in quantum theory, including areas like time-independent perturbation theory, time-dependent perturbation theory, and the variational method. A course such as Approximation Methods can provide exposure to these topics and more, assisting Quantum Information Scientists in advancing their understanding of quantum systems.
Data Scientist
Data Scientist
Quantum Computing Scientists work on the development of quantum computers and related technologies. One area of data science focuses on quantum machine learning, which utilizes quantum systems to enhance machine learning algorithms. Courses in quantum mechanics can help build a foundation in quantum theory, including areas like time-independent perturbation theory, time-dependent perturbation theory, and the variational method. A course such as Approximation Methods can provide exposure to these topics and more, assisting Quantum Computing Scientists in advancing their understanding of quantum systems.
Nanotechnologist
Nanotechnologist
Nanotechnologists are engineers and scientists who work in the field of nanotechnology, which involves the manipulation of matter at the atomic and molecular scale. Many nanotechnologies rely on principles of quantum mechanics to function. A course in quantum mechanics, such as Approximation Methods, can provide exposure to time-independent perturbation theory, time-dependent perturbation theory, the variational method, and more, which may be useful for Nanotechnologists.
Computational Physicist
Computational Physicist
Computational Physicists develop and apply computational techniques to solve problems in physics, often using numerical methods to study physical systems. Courses in quantum mechanics can help build a foundation in the subject, including areas like time-independent perturbation theory, time-dependent perturbation theory, and the variational method. A course such as Approximation Methods can provide exposure to these topics and more, assisting Computational Physicists in advancing their understanding of quantum systems and using these principles in computational methods.
Mathematician
Mathematician
Mathematicians study the properties of numbers, space, and other abstract concepts. Many Mathematicians who work in theoretical mathematics may find courses in quantum mechanics to be helpful. A course such as Approximation Methods can provide exposure to topics such as time-independent perturbation theory, time-dependent perturbation theory, and the variational method, which can be seen as applied mathematics with relevance in quantum systems.
Software Engineer
Software Engineer
Software Engineers design, develop, and test software systems. Many Software Engineers work on software for scientific and engineering applications, and some may find courses in quantum mechanics helpful for understanding the underlying principles of these applications. A course such as Approximation Methods can provide exposure to topics such as time-independent perturbation theory, time-dependent perturbation theory, and the variational method, which may be useful for Software Engineers working on quantum-based software systems.
For more career information including salaries, visit:
OpenCourser.com/course/tlszgq/approximation
Reading list
We've selected seven 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
Approximation Methods.
Modern textbook on quantum mechanics. It covers all of the topics that are covered in this course, and it does so in a clear and concise manner.
Well-written and comprehensive graduate-level textbook on quantum mechanics. It covers all of the topics that are covered in this course, and it does so in a clear and concise manner.
This is the classic textbook for learning quantum mechanics. It is well-written and comprehensive, and it covers all of the topics that are covered in this course. It is an excellent resource for students who want to learn more about quantum mechanics.
Good choice for students who want to learn more about quantum error correction.
Classic textbook on quantum mechanics. It good choice for students who want to learn more about the applications of quantum mechanics.
More mathematical treatment of quantum mechanics than the typical textbook. It good choice for students who have a strong background in mathematics and who want to learn more about the mathematical foundations of quantum mechanics.
Classic textbook on perturbation theory. It good choice for students who want to learn more about the mathematical foundations of perturbation theory.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/tlszgq/approximation
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Effort
Consists of 3 Modules, between 2 and 5 hours of work per module.
Level
Intermediate
Via
Coursera
Institution
University of Colorado Boulder
Instructor
Wounjhang Park
Language
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
- Approximation Methods (viewing)
- Foundations of Quantum Mechanics
Good to know
Suitable for individuals with a basic background in quantum mechanics who seek to enhance their understanding of approximation methods
Provides practical examples to demonstrate the effective application of each method
Enhances problem-solving capabilities by equipping learners to tackle various quantum mechanics issues using appropriate techniques
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