PHYS 631: Quantum Mechanics I (Fall 2023)


Instructor: Daniel A. Steck
Office: 277 Willamette      Phone: 346-5313      email: dsteck@uoregon.edu
Office hours: walk-in and by appointment (best to email first; I also try to answer questions by email quickly).
Teaching Assistant: Sean Ericson      office: WIL 251      office hours: W 11-12p (Th 11-12p in physics help room, Price B010)      email: sericson@uoregon.edu     

Course home page: https://atomoptics.uoregon.edu/~dsteck/teaching/23fall/phys631           qr

Schedule: MT 5-6:50p, 318 Willamette
Course reference number: 14322
Credits: 4
Prerequisites: none

Links: news, course notes, homework sets and keys.


Course overview

This course is a more-or-less standard introduction to quantum mechanics at the graduate level, one of the core components of your Ph.D. studies. This is the first of a 3-quarter sequence. This course will also assume you have studied quantum mechanics for at least one term at the undergraduate level.

Recommended Texts:

There is no required textbook to purchase for this course. The main reference for this course is the online text posted here.

Much of this material is also covered well in many other excellent texts. A few of the more widely used and/or interesting ones that you may want to have in your collection are:

Philosophy of This Course:

This is one of the core courses of your graduate physics training. This first course in the QM sequence covers mostly material that you should have already studied as an undergraduate. However, this course will cover this basic material at a higher, more rigorous level, building up the structure of QM from its basic axioms. In doing so you will likely uncover misconceptions and strengthen your understanding of the subject, while mastering the associated mathematical techniques (linear algebra, differential equations and boundary-value problems, approximation methods, regularization).

This course will in part be a traditional lecture course. But I'll also have work on exercises related to the material for the day (in small groups). These group exercises will happen in the last 30-45 minutes of each class. They will give you a chance to review/practice/discuss the material, and to have a chance to ask me more questions.

Study groups:

I highly encourage you to join/form a study group. If you need help in finding a study group, or you have already formed a group and you can take on more people, just let me know and I'll be happy to facilitate this.

While I encourage study groups, you must still work through problems on your own and turn in your own solutions—these groups work brilliantly for brainstorming, getting unstuck, clarifying, etc., but ultimately you have to work through the physics or you won't learn anything.


Grades

Grades for the course will be based on homework, a midterm exam, and a final exam. The relative weights will be as follows:

Electronic submission: you'll submit all documents electronically (via a web submission system). This includes solutions for homework, exercises, and exams. This will mean you will either need to type out solutions (preferably in LaTeX), or scan your (neatly) handwritten solutions. In the case of the dead-tree method, please make legible, data-efficient scans. Department scanners work well for this (contact me for details if you don't know what I mean), and home scanners work great too. Otherwise, use a scanner app for your phone or tablet (I've used Scanner Pro on iOS, which is cheap and works well, but there are many other cheap/free options available). Having this capability will serve you well beyond this class and this post-ish-pandemic era.

I'll also generally avoid giving out paper copies of homework, exercises, etc., so it would be good for you to bring a laptop or tablet to class if you want to refer to these.

Homework: there will be a total of 8 problem sets during the term. You'll submit these online, see the homework page for the upload link. The due dates for the homework assignments will be every Tuesday, to keep things simple (including exam week, but not during week 1 or midterm week/week 6).

Exercises: These are relatively simple problems related to the lecture material. These will be assigned during each lecture, when you'll start working on them, and they'll be posted on the notes page. You should turn in (online, see the notes page) your exercise solutions for each week all together, by the following Tuesday. I'll grade these on completion (i.e., if you do a reasonable job, you'll get full credit).

Midterm exam: The midterm exam will be held during the sixth week of class (30 October–3 November), details TBA.

Final exam: The final exam is scheduled for Monday, December 4, 7:15-9:15p. We'll work out the details in class towards the end of the term.

Pass/fail grading option: Since this is a core graduate course, you should take the graded option.


Syllabus

This is a tentative list of topics we will cover during this term. (I may change things up and substitute other topics.)

  1. Overview of mechanics in Hilbert space
  2. Operators and expectation values; uncertainty principle
  3. Matrix mechanics, unitary transformations, time evolution
  4. Free particle
  5. Square-well potentials
  6. Probability currents and tunneling
  7. Delta-function potential
  8. Double-well potentials, two-state dynamics, quantum Zeno effect
  9. Adiabatic transfer, adiabatic theorem, geometric phase, Aharonov-Bohm effect
  10. Harmonic oscillator, coherent states