This page is the syllabus for the graduate PHY 389 K class Quantum Mechanics (I) as taught in Fall 2023 by Professor Vadim Kaplunovsky (unique number 57825). Note: this class may differ from the 389 K classes taught in past or future semesters.

The main textbook for the class is *Modern Quantum Mechanics* by J. J. Sakurai;
my lectures would often (but not always) follow the chapters 1, 2, 3, and 5 of this book.
Although this texbook is not formally required for this class,
I strongly recommend you get a copy, preferabley the second edition.
If you cannot afford to buy a hard copy, there are pirated scans on the Internet: Google them up.

There are many other good graduate-level Quantum Mechanics textbooks, and I suggest you browse a few
of them in the library.
I personally like the *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

*Quantum Mechanics: an Introduction*by Thomas Banks,*Quantum Mechanics*by Cohen–Tannoudji, Diu and Laloë (volumes 1 and 2),*Quantum Mechanics: Fundamentals*by Kurt Gottfried and Tung–Mow Yan.

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.

Finally, if you have not learned the Complex Analysis in the undergraduate school,
you would need to catch up in a hurry:
This subject is an essential tool in almost all fields of Physics,
an many graduate classes (including mine) would presume you know at least the basics.
For a quick and dirty introduction to the sublect, I recommend the
*Schaum's Outlines: Complex Variables* by M. R. Spiegel,
S. Lipschuts, J. J. Schiller, and D. Spellman.

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 the 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.

- 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: they may be skipped or taught in extra lectures instead of the regular lectures.

This class is officially face-to-face, but I plan to shadow all the lectures online via Zoom and have them recorded for asyncronous viewing via Canvas. I strongly encourage all students to come to the lectures in person, but if you are sick please stay home and watch the lecture online.

There are 3 hours of regular lectures each week: 3:30 to 5 PM on Tuesdays and Thursdays, face-to-face in room PMA 5.116, mirrored on Zoom at https://utexas.zoom.us/j/93086124073.

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 in homeworks or exams.

I shall also give one or two extra lecture of a likbez type:
To explain a subject that the students *should* have learned in the undergraduate school, but some of them did not.

The extra lectures will be on Fridays from 3 to 4 PM. rougly every other week. Unlike the regular lectures, the extra lectures will be on-line only, via Zoom at https://utexas.zoom.us/j/93743087582. Note the different URL from the Zoom mirrors of the regular lectures.

Here is the *tentative* schedule of extra lectures —
**8/25, 9/8, 9/22, 9/29, 10/13, 10/20, 11/3, 11/17,** and maybe **12/1** —
and their subjects:

- Likbez lexture on
**8/25**:*Contour integrals and gaussian wave packets*.

Note unusual time and URL: 3:30 to 4:30 PM, at https://utexas.zoom.us/j/93875192586. - Extra lecture on
**9/8**:*Classical mechanics and its canonical quantization*. - Extra lecture on
**9/22**:*Identical bosons, second quantization, and non-relativistic quantum fields*. - Extra lecture on
**10/6**:*Bose–Einstein condensation and superfluidity.* - Extra lecture on
**10/20**:*Introduction to path integrals*. - Extra lecture on
**11/3**:*Information loss and density operators*. - Extra lecture on
**11/17**:*Density operators (2)*. - Extra lecture on
**12/1**: subject TBA.

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,
and spell out my *plan* for the next lecture.

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, and the final exam contributes 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 very hard*, much harder than in any undergradute class you have taken.

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.
If you email the scans rather than a PDF file, make sure to combine all the pages (of the same assignment)
into a single file.

The final exam is scheduled for December 7 (Thursday), from 3:30 to 6:30 PM (3 hours), in room ECJ 1.222.. The exam has to be taken in-person, you cannot take it online. If the exama time conflicts with with another exam you take or proctor, or with another obligation you cannot reschedule, let me know ASAP and I'll schedule your exam to a different time slot. Likewise, if you cannot come to the exam on time because of an illness or emergency, let me know ASAP and I'll do what I can to reschedule your exam.

The official exam schedule also a pre-scheduled time — December 9 (Saturday), 7 to 10 PM, room ECJ 1.304 —
for the make-up final exam for this class.
However, I shall use this time slot *only* if several students need it due to schedule conflicts;
but if only 1 or 2 students need a make-up exam, I may use a different time slot that would be more convenient
to the students and to myself.
So if you need to take the make-up exam for any reason, email me first and get a confirmed date.
Otherwise, if you miss the regular exam and simply show up on 12/9 without my confirmation, you might
end up in an empty room without the exam.

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: Professor Vadim Kaplunovsky.

- Office: PMA 9.314A, office phone (512) 471–4918.
- Office hours: Thursdays 2–3 PM..
- Email: vadim@physics.utexas.edu.

Please use email for*simple*homework questions or administrivia. Complicated physics questions should be asked in person or via Zoom. - If you need to reach me in a hurry, please email me your Skype ID or your WhatsApp number — or your phone number if you don't need the video link — and I'll call you back as soon as I can. Or catch me in the classroom right after a class.

Teaching assistant and grader: Sanjay Mathai.

- Email: sanjaym@utexas.edu.
- Office: PMA 9.316.
- Reserved office hours: Wednesday 11-12 AM.

Last Modified: November 14, 2023. Vadim Kaplunovsky

vadim@physics.utexas.edu