PHYS 580 :: Physics Illinois :: University of Illinois at Urbana-Champaign
Home page
1. General Information
Welcome to PHYS 580 Quantum Mechanics I
The course will be held in person at 144 Loomis Laboratory, on Mondays and Wednesdays, at 2:00 – 3:20 pm (US central time).
Jorge’s Office Hours: My office hours will take place on Fridays from 2:00 – 3:00 pm (US central time) at 437B Loomis Laboratory. You may also reach me at the same time using the recurring Zoom link for the course (see contact info). I strongly encourage you to use this opportunity to talk about physics with me (course topics, broader physics questions, you decide!). Feel free to contact me via email at other times as well, although an appointment will be probably needed given my other activities. In any case, remember that email is the best way to reach me.
TA Office Hours: Jordi Salinas San Martin = Tuesdays at 2 pm. Same Zoom link for the course.
The lectures will be recorded and they will be available via MediaSpace. Homework assignments will be available on the course web site.
2. Course Grading
Homework: Assignments will be distributed at regular intervals as much as possible. The lowest grade of the homework assignments will be dropped. I strongly recommend that you develop a regular schedule for doing these assignments, and do not wait until the due date before attempting the problems. Some of the problems can be quite tricky.
The homework assignments should be submitted via GradeScope. We will not accept homework by email. Questions about the grading of homework assignments should be directed to the TA first and, if the issue is not resolved, to me. Each assignment will have a due date, with late work penalized (10% decrease per week). If you know that you will have a conflict with the due date for some reason (conference, health issues, etc), please let me know in advance.
The homework is an essential part of the course; you cannot learn physics from just the lectures. The solutions to the homework will not be distributed, but the TA will provide constructive comments on your work so that you may learn from your mistakes.
Final exam: There will be no midterm, but there will be a final exam in the form of a take-home final.
1-hour research paper review: You will write a short review (which must not take you more than 60 minutes!) about some exciting paper you find on the web about quantum mechanics, broadly defined (you can search for papers using Google Scholar, iNSPIRE, or check APS journals, for instance). The detailed instructions for the review can be found here. Please follow the instructions so that you don't spend more than an hour doing this. The reviews will also be submitted via GradeScope. To get the full points, you have to submit 5 paper reviews throughout the course (you choose when you send them, but don't send more than one review per week).
Please understand that you will not be graded for your understanding of the papers you review. Rather, you will get the points by making an honest effort to fulfill the instructions, which will teach you an important skill that all scientists must have: efficient paper reading.
Grading: Final grade = 700 homework + 200 final (take-home) exam + 100 (reading assignment).
Maximum = 1000 points.
A >= 900
900 < B <= 800
800 < C <=700
700 < D <=600
F < 600
3. Pre-requisites
PHYS 580 is a graduate level quantum mechanics course, but the goal is to make it as much self-contained as possible. Nevertheless, you are strongly encouraged to have first attended an undergraduate physics course in quantum mechanics. For instance, the official Physics Department course website lists PHYS 485 or PHYS 487 as pre-requisites. A reasonable textbook that covers elementary undergraduate material is "Introduction to Quantum Mechanics" by D. J. Griffiths.
4. Textbooks
There is no official textbook for this course. However, you will have access to my handwritten notes right away on the course website (I'm trying to get all of it in PDF format ...). My notes are not meant to be a substitute for your own notes. Note-taking is a valuable and important skill to learn.
Here are some books that are traditionally recommended when it comes to a graduate level statistical mechanics course.
· R. Shankar, "Principles of Quantum Mechanics": Great book, very detailed, though it lacks more modern topics (e.g. quantum information).
· J. J. Sakurai, "Modern Quantum Mechanics": Excellent book, my favorite book when I was a student, though it lacks more modern topics (e.g. quantum information).
· S. Weinberg, "Lectures on Quantum Mechanics": It is a book by Weinberg. Therefore, one must read it (though his notation is not standard).
· L. D. Landau and E. M. Lifshitz, "Quantum Mechanics" (volume 3): A classic, old school book.
· Michael A. Nielsen and Isaac L. Chuang, "Quantum Computation and Quantum Information": Great book on quantum foundations and quantum information/computation.
· H.-P. Breuer and F. Petruccione, "The Theory of Open Quantum Systems": Great book on quantum foundations and open quantum systems.
· R. P. Feynman and A. R. Hibbs, "Quantum Mechanics and Path Integrals": Classic book about the path integral formulation of quantum mechanics.
5. Feedback
Please let me know if you have any suggestions or comments about the class, or if I mistakenly assume that you are familiar with some basic material. Your feedback is essential for this course - please enter in contact with me. There is no point in waiting until the end of the semester (or when you fill in a course evaluation!) because by then it is too late for me to consider acting on the feedback.
6. Course Outline
This is the basic plan (there can always be a few changes here and there).
Review of the math of quantum mechanics (Hilbert spaces of finite and infinite dimension).
Review of classical mechanics: Principle of least action, Noether’s theorem and symmetries, Hamilton formalism, Poisson brackets, canonical formalism, infinitesimal canonical transformations/symmetries, Hamilton-Jacobi equation.
Foundations of quantum mechanics: Postulates, measurement process, commuting and non-commuting observables, uncertainty principle, Schrodinger vs. Heisenberg pictures, Ehrenfest theorem, path integrals in quantum mechanics/propagators, gauge transformations in quantum mechanics, Aharonov-Bohm effect, adiabatic theorem, Berry's phase.
Density matrices: General properties, purity, mixed states, von-Neumann equation, coherence, simple models of decoherence, composite quantum systems, entanglement, quantum measurements in composite systems, Einstein-Podolski-Rosen, Bell’s inequality, no cloning theorem, density matrices from entanglement, partial trace, Schmidt decomposition, purification, generalized quantum measurements vs. projective measurements, POVMs and Kraus operators, von Neumann entropy, mutual information, open quantum systems, and the Kraus representation theorem.
Symmetries in quantum mechanics: Discrete vs. continuous symmetries.
7. Academic Integrity
As a student it is your responsibility to refrain from infractions of academic integrity, from conduct that may lead to suspicion of such infractions, and from conduct that aids others in such infractions. A short guide to academic integrity issues may be found at https://provost.illinois.edu/policies/policies/academic-integrity/students-quick-reference-guide-to-academic-integrity/ . The authoritative source is the Student Code. I will enforce the University's standards of academic integrity.
8. Disability Access
The Department of Physics is committed to being an open and welcoming environment for all of our students. We are committed to helping all of our students succeed in our courses.
To obtain disability-related academic adjustments and/or auxiliary aids, students with disabilities must contact the course instructor and the Disability Resources and Educational Services (DRES) as soon as possible. To contact DRES, you may visit 1207 S. Oak St., Champaign, call 333-4603, e-mail disability@illinois.edu or go to the DRES website. If you are concerned you have a disability-related condition that is impacting your academic progress, there are academic screening appointments available on campus that can help diagnosis a previously undiagnosed disability by visiting the DRES website and selecting “Sign-Up for an Academic Screening” at the bottom of the page.
9. Assistance for Academically Related and Personal Problems
Most college offices and academic deans provide academic skills support and assistance for academically related and personal problems. Links to the appropriate college contact can be found by going to this website and selecting your college or school: http://illinois.edu/colleges/colleges.html
If you are experiencing symptoms of anxiety or depression or are feeling overwhelmed, stressed, or in crisis, you can seek help through the following campus resources:
Counseling Center
206 Fred H. Turner Student Services Building
7:50 a.m.-5:00 p.m., Monday through Friday
Phone: 333-3704
McKinley Mental Health
313 McKinley Health Center
8:00 a.m.-5:00 p.m., Monday through Friday
Phone: 333-2705
McKinley Health Education offers individual consultations for students interested in learning relaxation and other stress/time management skills, call 333-2714.