This page is the syllabus for the graduate PHY 389 K class Quantum Mechanics (I) as taught in Fall 2021 by Professor Vadim Kaplunovsky (unique number 57550). Note: this class may differ from the 389 K classes taught in past or future semesters.

Covid–19 notice

Despite the current delta-wave of covid–19 epidemic, the UT adminstration wants most classes this Fall to work in the face-to-face-in-the-classroom mode. However, if the epidemic worsens, the administration may decide to switch to the hybrid, blended, of fully online modes. In particular, this class will start in the face-to-face mode, but later in the semester it might switch to the hybrid or online modes.

Meanwhile, please follow all the covid–19 safety measures. In particular:

For your information, I am vaccinated (2 shots of Pfizer vaccine). I shall try wering a mask while in class, but if it interferes with my speaking — or with you hearing my lecture, — I would have to take it off. So for your safety, please do not sit too close to the lectern.

Textbook and Supplementary Notes

There is no required textbook for the class, but I strongly recommend Modern Quantum Mechanics by J. J. Sakurai as my lectures would often (but not always) follow the chapters 1, 2, 3, and 5 of that book. If you cannot find a hard copy of this book, there are pirated copies on the Internet, Google them up.

Other good textbooks I recommend are Lectures on Quantum Mechanics by Steven Weinberg — it's based on the class he taught here at UT a few years ago, — and Quantum Mechanics by A. S. Davydov. The Davydov's book is old-fashioned and starts with the undergraduate-level basics, but it eventually gets to the advanced subjects. Also, other professors who taught this class recommend

Besides the textbook, I shall occasionally write my own supplementary notes or download them from the Internet. All such notes will be linked to this page.

Prerequisites and Presumed Knowledge

The formal prerequisite for the 389 K Quantum Mechanics (I) class is graduate standing. The undergraduate students who have already taken the 373, 362 K and 362 L classes are welcome to audit the class, but please talk to me before you take it for credit.

Since 389 K is a graduate class, I presume the students have already learned the undergraduate-level quantum mechanics — a lower-division Modern Physics class followed by at least one upper-division QM class, although additional QM or applied QM classes would be very helpful. But of course it's your knowledge which counts rather than the classes you have taken, so if you have learned enough QM by yourself you should be OK. If you have learned — and I mean really learned — physics and math in first part (chapters 1–5) of David Griffith's Introduction to Quantum Mechanics you should be ready for my class, and if you are somewhat familiar with the material in the second path of that book, so much the better.

Math-wise, I expect the students in my class have basic knowledge of partial differential equations and of the complex analysis.

Course Content

Basic Physical and Mathematical Concepts of QM:
Quantum states and the Hilbert space; observables, operators, bases and matrices; commutation relations and uncertainty rules; qubits, entanglement, and density matrices.
Quantum Dynamics:
Schrödinger and Heisenberg-Dirac equations; canonical quantization; quantization of the harmonic oscillator and the creation/annihilation operators; lasers*.
Wave Mechanics:
Bound and unbound states; reflection, tunneling and scattering; semi-classical WKB approximation; coupling to electromagnetic fields and gauge invariance; Aharonov-Bohm effect, SQUIDs and magnetic monopoles*; path integrals*.
Symmetries, especially Rotations and Angular Momentum:
Translations in space and the momentum operator; rotations and the J operator; commutation relations and the spectrum of the angular momentum; representations, spin and the SU(2) group; orbital angular momentum and the central potential; adding angular momenta; tensors and Wigner-Eckart theorem; general continuous symmetries -- groups, generators, commutation relations and representations*; parity and other discrete symmetries*.
Perturbation Theory:
Time-independent perturbations, non-degenerate and degenerate; fine structure; Born-Oppenheimer theory of molecules*; time-dependent perturbations and quantum transitions; Fermi's Golden rule; intruduction to scattering*.

The subjects marked with a * are optional and will be taught in extra lectures.


This class has 3 hours of regular lectures each week: 3:30 to 5 PM on Tuesdays and Thursdays, face-to-face in room ASE 1.124. If later in the semester the class becomes on-line or hybrid, I shall post the Zoom URL right here.

Update 9/22: Starting Thursday 9/23, all the regular lectures will be shadowed via Zoom at https://utexas.zoom.us/j/99005756099. I encourage all students to attend the lectures in person, but if you cannot make it physically then come in virtually via Zoom.

Note: all the Zoom shadowed lectures are recorded — both video an voice —, and you can find these recording on Canvas.

Update 10/1: Since the first 8 regular lectures were not recorded, the Adad Hussain (the TA) scanned my notes for those lectures, or rather of the notes I wrote under the document camera. These scans can be found here.

Note: the scans do not include my online notes or other online material; those notes are available here. And wherever I said without writing it down did not get recorder; sorry.

Extra Lectures

Besides the regular lectures, I shall give a few extra lectures — roughly every other week — about subjects that are somewhat ouside the main focus of the course but are interesting for their own sake, such as magnetic monopoles or path integrals. The students are strongly encoraged to attend the extra lectures, but there is no penalty for missing them. The issues covered by extra lectures will not be necessary to understand the regular lectures and will not appear on exams.

The extra lectures will be on Fridays, from 12 noon to 1 PM, on 9/3, 9/17, 10/1, 10/15, 10/22, 11/5, 11/19, and maybe 12/3. The extra lectures are going to be online via Zoom https://utexas.zoom.us/j/98117292886. Please note: this is a different link than the regular lectures.

Lecture Log

For students' convenience, I shall keep a log of lectures and their subjects on this page. Since the pace of the course may change according to the students' understanding, I will not make a complete schedule at the beginning of the class. Instead, I will simply log every lecture after I give it. This way, if you miss a lecture, you will know what you should read in the textbook and other students' notes.

Grades, homeworks, and exams

The grades for this class will be based on the homeworks and the final exam; there will be no midterm exams. The homeworks (11 best out of 13) contribute 50% of the grade, the final exam the other 50%.

Besides affecting your grades, the homeworks are absolutely essential for understanding the course material. Often, due to the time pressure, I will explain the general theory in class and leave the examples for the homework assignment. It is extremely important for you to work them out by yourselves; otherwise, you might think you understand the class material but you would not! Be warned: The homeworks will be rather hard.

I shall post homework assignments roughly once a week and post them (or rather link them) to this page. The solutions will be linked to the same page after the due date of each assignment.

I shall collect the homeworks in class on the day they are due. If you cannot come to class for some reason, please scan your homework (or take clear pictures with your phone) and email them to me and to the TA.

Updated 11/29: The final exam is currently scheduled for December 11 (Saturday), 9–12 AM, in the regular classroom ASE 1.124. However, this schedule might change in the next few days (the last week of the semester) since it conflicts with the final exam for another class (graduate Classical Mechanics) currently scheduled for the same time slot. If this happens, I'll let the students know ASAP; but just to make sure, please double-check you exam schedule on the last class day of this semester.

Updated 12/2: Apparently, it's the other class's exam that been rescheduled, while the schedule for out final exam remains unchanged: December 11 (Saturday), 9–12 AM, in the regular classroom ASE 1.124.

Unlike the regular classes, the exam cannot be taken on-line; you must physically come to class on the exam day. If you are sick, or have other kind of emergency preventing you from coming to the exam, please let me know ASAP and I'll work out an alternative arrangement.

The final exam will be comprehensive — it may include any subject taught in class from the first lecture to the last (but not the extra lectures). During the exam, you may use open books and/or notes. However, if your books or notes are in electronic form, they must be downloaded before the exam. To make sure your exam is your own work, the Internet connection on all laptops, tablets, etc., must be turned off during the exam, and the cellphones must be completely turned off.

Instructor and Asisstant

Instructor: Professor Vadim Kaplunovsky.

Teaching assistant and grader: Asad Hussain.

Last Modified: December 1, 2021.
Vadim Kaplunovsky