Foundations of Quantum Mechanics from Coursera

This course can also be taken for academic credit as ECEA 5610, part of CU Boulder’s Master of Science in Electrical Engineering degree.

This course covers the fundamental concepts and topics of quantum mechanics which include basic concepts, 1D potential problems, time evolution of quantum states, and essential linear algebra. It provides undergraduate level foundational knowledge and build on them more advanced topics.

At the end of this course learners will be able to:

1. demonstrate full grasp of basic concepts in quantum mechanics including wave-particle duality, operators and wavefunctions, and evolution of quantum states,

2. achieve mastery of the mathematical apparatus needed for quantum mechanics and

3. attain foundational knowledge required to learn more advanced quantum mechanics and applications.

What's inside

Syllabus

Wave-particle Duality and Schrödinger Equation

In this module we will introduce the course and the Quantum Mechanics for Engineers specialization. In addition, we will discuss wave-particle duality, time-independent Schrödinger equation. one-dimensional infinite potential well problem, properties of eigensolutions and Hilbert space.

One-dimensional Potential Problems

In this module, we will solve several one-dimensional potential problems. They include finite potential well, harmonic oscillator, potential step and potential barrier. We will discuss the physical meaning of the solutions and highlight any non-classical behaviors these problems exhibit.

Operators and Measurements 1

This module covers the theory of measurements in quantum mechanics. We start our discussion by introducing Stern-Gerlach experiment and the difficulty in interpreting the results classically. We then develop mathematical tools required to properly describe the results and then apply them to the interpretation of Stern-Gerlach experiments.

Operators and Measurements 2

In this module we expand upon the discussion from the previous module and introduces Hamiltonian, position and momentum operators and the uncertainty principle that governs the relationship between the operators. We also discuss the general principle of change of basis and the specific example of position and momentum representations.

Time Evolution of Quantum States

This module discusses how to describe the time-evolution of a quantum system. There are two equivalent methods, Schrödinger and Heisenberg pictures, where the time evolution can be obtained by the time-dependent Schrödinger equation and Heisenberg equation of motion, respectively. We will discuss the specific example of harmonic oscillator and finally introduce the particle current.

Ensembles and Identical Particles

This module discusses how to deal with ensembles. We will first discuss the difference between pure and mixed states and how to use the density matrix to describes them. We then discuss indistinguishable particles and exchange interaction, which eventually lead us to the thermal distribution functions.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Suitable for undergraduates majoring in electrical engineering

Provides foundational knowledge in quantum mechanics

Covers essential linear algebra for quantum mechanics

Builds a strong foundation for advanced topics in quantum mechanics

Taught by Wounjhang Park, a respected expert in quantum mechanics

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 Foundations of Quantum Mechanics with these activities:

Connect with Quantum Experts

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Expand your network by reaching out to experts in the field of quantum computing to gain insights and guidance.

Browse courses on Quantum Computing

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Attend industry events or conferences to meet professionals in the field.
Reach out to researchers or practitioners via LinkedIn or email.
Join online communities and forums dedicated to quantum computing.

Re-read High School Level Math

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Quantum mechanics has many mathematical concepts that you need to make use of already. This activity helps you revive your understanding of elementary mathematics.

Browse courses on Mathematics

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Review your high school textbooks.
Practice on some online quizzes or exercies.
Ask for help from any math teachers or peers that you know.

Review Linear Algebra

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Review fundamental concepts of linear algebra including vector spaces, matrices, transformations, and eigenvalues to refresh knowledge for this course.

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Review notes and textbooks from previous courses on linear algebra.
Complete practice problems and exercises to reinforce concepts.
Attend a workshop or tutorial on linear algebra to refresh understanding.

Six other activities

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Watch Video Lectures on Quantum Mechanics by Leonard Susskind

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These video lectures provide a clear and concise overview of the basic concepts of quantum mechanics.

Browse courses on Quantum Mechanics

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Visit the website of The Stanford Encyclopedia of Philosophy.
Click on the link to 'Quantum Mechanics'.
Watch the video lectures by Leonard Susskind.

Read 'Quantum Mechanics for Mathematicians' by James Glimm and Arthur Jaffe

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This book provides a mathematical approach to quantum mechanics that will help you from the mathematics side of the course.

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Read through the book.
Work on the exercises at the end of each chapter.
Attend the office hours of the course instructor to ask any questions.

Explore Quantum Computing

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Gain a foundational understanding of quantum computing concepts and applications by following guided tutorials and online courses.

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Enroll in an introductory course or tutorial on quantum computing.
Follow online tutorials and demonstrations to learn about quantum gates, algorithms, and hardware.
Experiment with quantum computing simulators to gain hands-on experience.

Solve Quantum Mechanics Problems

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Enhance your problem-solving skills in quantum mechanics by practicing a variety of exercises and challenges.

Browse courses on Quantum Mechanics

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Collect practice problems from textbooks, online resources, or previous coursework.
Attempt to solve the problems independently, referring to course materials for support.
Review your solutions and identify areas for improvement.

Build a Quantum Circuit Simulator

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Deepen your understanding of quantum computing by designing and implementing a simple quantum circuit simulator, enabling you to visualize and explore quantum algorithms.

Browse courses on Quantum Computing

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Learn a programming language suitable for quantum computing, such as Qiskit or Cirq.
Design a basic quantum circuit simulator using the chosen programming language.
Implement the simulator, including functionality for creating and manipulating quantum circuits.
Test and debug the simulator to ensure it accurately simulates quantum circuits.

Build a Model of a Quantum System

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Building a model of a quantum system will help you to develop a deeper understanding of the system's behavior.

Browse courses on Quantum Mechanics

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Choose a quantum system that you are interested in.
Research the system and gather information from reliable sources.
Build a model of the system using a software program or other tools.

Career center

Learners who complete Foundations of Quantum Mechanics will develop knowledge and skills that may be useful to these careers:

Quantum Computing Research Scientist

The field of quantum computing is still in its early stages of development, but it has the potential to revolutionize many industries, including healthcare, finance, and materials science. A Quantum Computing Research Scientist researches and develops new algorithms and applications for quantum computers. This course on the Foundations of Quantum Mechanics can provide you with knowledge of the fundamental concepts of the field and prepare you to pursue a career in quantum computing research.

See salaries and explore the career path for Quantum Computing Research Scientist

Theoretical Physicist

Theoretical physicists develop and test theories about the fundamental nature of the universe.

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Quantum Information Scientist

Quantum information scientists work on the development of new quantum technologies, such as quantum computers and quantum cryptography.

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Materials Scientist

Materials scientists research and develop new materials for various applications.

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Optical Engineer

Optical engineers design and develop optical systems for applications in telecommunications, imaging, and other fields.