PHGN 520: Quantum Mechanics I (SPRING 2013)



Instructor
Prof. Zhigang Wu
Office: 443 Meyer Hall
Phone: (303) 2733068
E-Mail: zhiwu@mines.edu

Lecture Location and Time
205 Berthoud Hall; Mondays, Wednesdays & Fridays @ 10:00--10:50 AM

Teaching Assistant
Torey Semi; MH 475; tsemi@mines.edu

Office Hours
  • Mondays @   3:00 --   4:00 PM
  • Tuesdays @   3:00 --   4:00 PM
  • Fridays    @ 11:00 -- 12:00 AM
  • You need to make an appointment for other time slots.



Syllabus
Here you can find the lecture notes, schedule, extra documents, assignments, solutions, etc.

Contents
This is the first part of the graduate course in quantum mechanics, focusing on fundamental quantum theory and practical approximate methodas, and their applications to simple 1D and 3D systems.

The main topics are:
  • Formal quantum theory, Hilbert space
  • Simple 1D quantum systems, simple harmonic oscillators
  • Quantum dynamics, Hensenberg picture, spin precesion
  • 3D quantum systems, central potential, Coulomb potential
  • Angular momentum, spin, and quantum rotation
  • WKB and time-independent perturbation theory
Prerequisites
  • PHGN 511: Mathematical Physics
  • PHGN 320: Modern Physics II (Introduction to Quantum Mechanics)
Class Policies and Suggestions
  • I expect all students to attend every class. The statistics show that those seldom attend often get low scores.
  • If you have anything unclear, raise your hand and interrupt me immediately. You cannot afford failing to understand any derivations or concepts. Do not let your confusion build up, go to my office and ask me; otherwise you will get totally lost.
  • Ipads, laptops, cell-phones, and other electronics are strictly forbidden during the class. Students using these devices frequently in classes performed poorly.
  • Please go to my office often, not merely for homework problems.
  • I expect you to spend about 12 to 15 hours weekly to study the contents (5-7 hours) and finish homework (6-8 hours). If you use a lot more than 15 hours per week, please let me know and I will try to help you out.
  • If you have any suggestions, concerns, worries, frustrations, etc, please let me know as soon as possible. You may send me email, talk to me personally, or contact the class coordinators (Roxanne Tutchton & Ariel Bridgeman).
  • The class coordinators are responsible for contacting me immediately if they have any feedback from the class. She/he will meet me at the begining of February, March, and April.



Homework Assignments
  • Homework will be assigned on every Tuesday (except for the test weeks), due on the next Wednesday at 10 AM.
  • Late due homework will get ZERO point, so just submit even incomplete.
  • But you can turn in homework late (up to 2 days before 5 PM Friday) twice during the semester without any reasons.
  • You need extraordinary reasons to get my permission to turn in late more than twice or two days each time.
  • You need to let me know 24 hours before the due time for any delay and get permission beyond the limit.
  • Totally there are about 12 assignments.
  • Clear and detailed derivations are crucial to get good scores.
  • Please try NOT to use Mathematica if possible. Mathematica is a great tool for visulization, solving complicated while trivial problems like matrix diagonalization, etc, but relying on it will hurt your analytical skills.
  • I will try to inspect the graded homework as much as possible.
  • Go to my office to get homework grading errors corrected. But you need to do so within one week after you get your graded assignments back.
Academic Integrity
Homework assignments have to be done INDEPENDENTLY. Group discussions are encouraged but you still need to finish the problems by yourself, and report it in your notes. If you use any materials from papers, online resources, and books other than the textbook, please also report in your notes. No deduction will be made if you report; otherwise I treat it as an academic integrity violation.

Exams
  • Three exams will be scheduled: two one-hour in-class mid-terms and a two-hour final.
  • About 1/4-1/3 of problems in exams are taken directly from homework assignments.
  • Exams are closed-book, with essential equations and formulae provided (should be more than you actually need).
  • If you have hard time memorizing an equation or formula, it means they will be given in the tests if needed.
  • Go to my office to get test grading errors corrected. But you also need to do so within one week after you get your graded tests back.
Grading
Homework (45%) + Midterm Exam (2 × %15) + Final Exam (25%)
A: ≥ 95%, A-: 90-94%; B+: 87-89%, B: 83-86%, B-: 80-82%
C+: 77-79%, C: 73-76%, C-: 70-72%; D: 60-69%; F: 0-59%

In practice, the class is graded on a modified curve, so that the average is about 85% or better. Any modifications will be only upwards, and be applied to everyone equally. Specifically, the average of every exam (120 points each) will be adjusted at least equal to 75 by adding a common number to everyone. The homework average is expected to be much higer than 80 (last year, PHGN 520 was 87 and PHGN 521 was 91), so normally no adjustment is required. If necessary, more points will be added to each of you until about 2/3 are B or better (including B, B+, A- and A).
  • A: Understanding the contents very well, excellent in both exams and homework assignemnts.
  • B: Understanding the contents well, good in exams, and homework is about the average.
  • C: Understanding the contents poorly, exams are way below average, and homework is around or below average.
  • D: Usually I won't give you a D. C is awful already. I give a D only if you meet all these (I guess it is pretty hard): seldom finish homework, seldom appear in classroom, hardly work out any problems in the tests.



Textbook
Modern Quantum Mechanics, by J. J. Sakurai and J. J. Napolitano, Addison Wesley, 2nd Edition, 2010.



Recommended Books
  • Lectures on Quantum Mechanics, by S. Weinberg, Cambridge University Press (November 30, 2012).
  • This is a brand new textbook written by Steven Weinberg, Nobel laureate in physics and probably the most important living physicist. I like this book very much.

  • Quantum Mechanics with Basic Field Theory, by B. R. Desai, Cambridge University Press, 2009.
  • This is a modern QM textbook, covering the basic field theory which normally is not presented by other textbooks. But this version has a lot of typos, and it is pretty dry -- no enough explanations and physical motivations.

  • Quantum Mechanics in a Nutshell, by G. D. Mahan, Princeton University Press, 2008.
  • This is also a modern QM textbook, covering many latest developments and interesting applications of QM, particularly in condensed matter physics. But it is not an easy book for graduate students.

  • Quantum Mechanics: Fundamentals, by K. Gottfried and T.-M. Yan, Springer, 2nd Ed, 2004.
  • Probably the best QM textbook for graduate students.

  • Quantum Mechanics, by E. Merzbacher, Wiley, 3rd Ed, 1997.
  • A classical QM textbook, very well written and easy to read. But it is slightly outdated.

  • Principles of Quantum Mechanics, by R. Shankar, Springer, 2nd Ed, 1994.
  • An excellent textbook for QM I, but it lacks the depth for QM II.

  • Quantum Mechanics Non-Relativistic Theory, by Landau and Lifshiz, Butterworth-Heinemann, 3rd Ed, 1981.
  • A great book for theoretician, but it is outdated now.

  • Quantum Mechanics, by A. Messiah, North-Holland, 1959; Dover, 1999.
  • One of the best QM textbooks so far, covering a wide range of traditional topics thoroughly.