Physics 162: Quantum Mechanics#
These are the lecture notes for Physics 162a and 162b at Brandeis University. PHYS 162 is a two-semester sequence that is required for first-year Physics graduate students. The course covers nonrelativistic quantum mechanics as well as some basic concepts in classical mechanics.
The textbook used for this course (as of the time of writing these notes) is Quantum Mechanics: An Experimentalist’s Approach by Eugene Commins [Commins, 2014], essentially the textbook version of the author’s very popular course at UC Berkeley. These notes represent my own take on the subject matter, based on some 33-odd years (counting my own PhD studies) as a theoretical physicist. The student is encouraged to consult a variety of textbooks on a given subject, as well as their classmates and professor.
The first semester will focus on the basic axioms and structure of quantum and classical mechanics, illustrated by simple examples, mostly from one-dimensional non-relativistic particle mechanics. The second semester will consider more advanced concepts and techniques, including the Feynman path integral, the rotation group, various approximation schemes, and systems of multiple identical particles. It will also focus more on real-world examples (albeit often crudely modeled) from atomic and condensed matter physics. A note for any outside readers: if you find this useful, that’s awesome. Note that these lectures are the result of a dynamic interaction with the particular students I teach, and will skip over in-class activities aimed at cementing their knowledge. Finally these are not going to be completely clean, especially for now; they are the typed equivalent of written lecture notes, done so that I can more easily update in future classes.There will be lots of mistakes, hopefully mostly (but not entirely) typos, which shoulkd get ironed out with repeat use and complaints.
The picture is a portrait of Carl Eckart, and is something of a personal reference. As I type this I have been working more and more in physical oceanography. However even within oceanpgraphy I have not left quantum mechanics behind. Eckhart himself was a well-regarded quantum physicist, famous among other things for the Wigner-Eckart theorem which we will cover here. During WWII he worked on submarine detection and after the war became a professor of geophysics at the Scripps Institute of Oceanpgraphy, where he became a distinguished oceanographer. One hope, as I develop these notes, is to point out interesting points of contact between quantum mechanics and other subjects.