Note: This course will not count for or substitute for any course prefixed by PHYS.
Prerequisites: Students should be comfortable with calculus and linear algebra. Homeworks for this course will involve solving algebraic equations involving matrices. All math concepts required will be fully reviewed, but not in enough detail for a student to learn it all from scratch. Students should also be comfortable with basic ideas from probability and statistics, which are fundamental to the quantum mechanical description of nature.
Quantum mechanics is the most successful physics theory ever devised. It is also probably the most counter-intuitive. As a result, there is a certain air of mystery about it. In this course, we will dispel that mystery. We will certainly cover Heisenberg’s Uncertainty principle, and much more! We will work through the basic ideas of measurement and observation, energy and energy scales, Schroedinger’s cat, and wave-particle duality, as well as current ideas such as quantum computing, entanglement and non-locality. At the end of the course, we will discuss (but not master) topics related to string theory, black holes, quantum gravity, and dark matter. We will also discuss quantum mechanics in the context of DNA, proteins, and molecular machines.
In this course, we will develop the ideas of quantum mechanics pedagogically rather than historically. That is, instead of starting with 19th century physics and obscure experimental results that eventually led to the discovery of quantum mechanics, we will approach the subject from the point of view of lotteries, coin flips, and gambling. Specifically, students will learn that quantum mechanics can be understood simply as an alternative mathematical approach to probability. The resulting alternative rules of probability describe quantum mechanical processes and systems, in just the way that conventional rules of probability describe processes in the everyday world.
There will be mathematical problems assigned for homework. Students will be encouraged to work in teams, but each student will be responsible for mastering the homework problems, which may be the subject of short quizzes in class. The reason for this was laid out by no less than Richard Feynman — to understand physics, you have to do some calculations. There is just no substitute.
Apart from simple in-class quizzes designed to be sure students mastered the homework problems, there will be no in-class examinations. Instead, each student will be required to write two papers and to make at least one presentation to the class. Class meetings will typically be interactive rather than lecture-based. Textbooks will be suggested but not required — there is plenty of online material about quantum mechanics.