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Approximation Methods

Approximation Methods

This course is part of Quantum Mechanics for Engineers Specialization

Instructor: Wounjhang Park

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3 modules

Gain insight into a topic and learn the fundamentals.

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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.

14 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

Distinguish non-degenerate and degenerate cases and use appropriate methods.
Perform calculations using the time-independent perturbation theory.
Describe absorption and stimulated emission processes.
Obtain approximate solutions using the variational method.

Skills you'll gain

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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

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There are 3 modules in this course

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.

Module details

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.

What's included

8 videos6 readings1 assignment2 discussion prompts

8 videosTotal 107 minutes

Course Introduction2 minutes
Non-degenerate Perturbation Theory17 minutes
Second Order Correction11 minutes
Stark Effect16 minutes
k-dot-p Method15 minutes
Degenerate Perturbation Theory16 minutes
Fine Structure13 minutes
Zeeman Effect17 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 150 minutes

Homework #1150 minutes

2 discussion promptsTotal 20 minutes

Introduce Yourself!10 minutes
Two-state System10 minutes

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.

What's included

5 videos3 readings1 assignment1 peer review

5 videosTotal 71 minutes

Interaction Picture16 minutes
Time-dependent Two-state Problem9 minutes
Time-dependent Perturbation Theory13 minutes
Transition Probability 113 minutes
Transition Probability 219 minutes

3 readingsTotal 21 minutes

Module Topics1 minute
Physical Constants10 minutes
Entering Math Expressions10 minutes

1 assignmentTotal 150 minutes

Homework #2150 minutes

1 peer reviewTotal 60 minutes

Rabi oscillation60 minutes

This module covers several non-perturbative approximation methods. They are the tight binding method, variational method and the use of finite basis set.

What's included

3 videos3 readings1 assignment1 discussion prompt

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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