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 is part of the Quantum Mechanics for Engineers Specialization
Offered By
About this Course
Undergraduate-level calculus, differential equations and linear algebra
What you will learn
Understand the quantum mechanical meaning of wave-particle duality
Calculate probabilities and expectation values for physical observables
Use both Schrödinger and Heisenberg picture to solve for time evolution of quantum states
Describe fermions and bosons using multiparticle basis functions.
Skills you will gain
- Differential Equations
- Quantum Measurement
- Linear Algebra
Undergraduate-level calculus, differential equations and linear algebra
Offered by

University of Colorado Boulder
CU-Boulder is a dynamic community of scholars and learners on one of the most spectacular college campuses in the country. As one of 34 U.S. public institutions in the prestigious Association of American Universities (AAU), we have a proud tradition of academic excellence, with five Nobel laureates and more than 50 members of prestigious academic academies.
Start working towards your Master's degree
Syllabus - What you will learn from this course
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.
About the Quantum Mechanics for Engineers Specialization
This Specialization is intended for engineers seeking to acquire fundamental understanding of quantum mechanics which are the basis of modern electrical, mechanical and quantum engineering. Through 3 courses, you will learn (1) basic concepts such as superposition and entanglement of quantum states, measurement in quantum mechanics and uncertainty principle, (2) mathematical tools needed to describe and manipulate quantum states, (3) advanced theory of angular momentum and (4) approximation methods widely applicable in many fields.

Frequently Asked Questions
When will I have access to the lectures and assignments?
What will I get if I subscribe to this Specialization?
Is financial aid available?
More questions? Visit the Learner Help Center.