PHGN 521: Quantum Mechanics II (FALL 2015)

Prof. Zhigang Wu
Office: 443 Meyer Hall
Phone: (303) 2733068

Lecture Location and Time
204 Hill Hall; Mondays, Wednesdays & Fridays @ 11:00 -- 11:50 PM

Teaching Assistant
Xiaoning Zang; Email:

Office Hours
  • Mon. @   4:00 --   5:00 PM
  • Tue.   @   3:00 --   4:00 PM
  • Wed. @   4:00 --   5:00 PM
  • You need to make an appointment for other time slots.

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

This is the second part of the graduate course in quantum mechanics, focusing on the applications of the basic theory introduced in QM I and approximation methods to electromagnetic radiation, quantum scattering, etc, together with theory of symmetry and quantum entanglement.

The main topics are:
  • WKB, variational principle
  • Time-independent and time-dependent perturbation theory
  • Electromagnetic radiation, the second quantization
  • Quantum scattering, Born approximation, partial waves
  • Symmetry, Wigner-Eckart theorem
  • Quantum interpretation and entanglement
Prerequisites 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 10 to 15 hours weekly to study the contents (4-6 hours) and finish homework (6-9 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 (TBD). The class coordinators are responsible for contacting me immediately if they have any feedback from the class.

Homework Assignments
  • Homework will be assigned on Wednesday, due on next Thursday at 5 PM to TA's mailbox.
  • Late due homework will get ZERO point, so just submit even incomplete.
  • You can turn in homework late (at 9 AM the following Monday to my office) twice without any reasons.
  • You need extraordinary reasons to get my permission to turn in late more than twice or later than Monday 9 AM.
  • You need to email me 24 hours before the due time for any delay and get permission if beyond the limit.
  • Totally there are 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.
  • But you can use Mathematica if not explicitly written in a problem.
  • I will try to inspect the graded homework as much as possible.
  • Go to my office to get homework grading errors corrected within one week after you get your 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.

The Colorado School of Mines affirms the principle that all individuals associated with the Mines academic community have a responsibility for establishing, maintaining an fostering an understanding and appreciation for academic integrity. In broad terms, this implies protecting the environment of mutual trust within which scholarly exchange occurs, supporting the ability of the faculty to fairly and effectively evaluate every student's academic achievements, and giving credence to the university's educational mission, its scholarly objectives and the substance of the degrees it awards. The protection of academic integrity requires there to be clear and consistent standards, as well as confrontation and sanctions when individuals violate those standards. The Colorado School of Mines desires an environment free of any and all forms of academic misconduct and expects students to act with integrity at all times.

Academic misconduct is the intentional act of fraud, in which an individual seeks to claim credit for the work and efforts of another without authorization, or uses unauthorized materials or fabricated information in any academic exercise. Student Academic Misconduct arises when a student violates the principle of academic integrity. Such behavior erodes mutual trust, distorts the fair evaluation of academic achievements, violates the ethical code of behavior upon which education and scholarship rest, and undermines the credibility of the university. Because of the serious institutional and individual ramifications, student misconduct arising from violations of academic integrity is not tolerated at Mines. If a student is found to have engaged in such misconduct sanctions such as change of a grade, loss of institutional privileges, or academic suspension or dismissal may be imposed.

  • Three exams will be scheduled: two one-hour in-class mid-terms and a two-hour final.
  • Problems in exams are similar to those in 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 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.
Homework (50%) + Midterm Exams (2 × %15) + Final Exam (20%)
A: ≥ 95%, A-: 90-94%; B+: 85-89%, B: 80-84%
B-: 75-79%; C+: 70-74%, C: 65-69%, C-: 60-64%
D+: 55-59%; D: 50-54%; D-: 45-49%; F: 0-44%

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 (125 points each) will be adjusted at least equal to 80 by adding a common number to everyone. The homework average is expected to be much higer than 80 (last year, PHGN 520 was 92 and PHGN 521 was 87), so normally no adjustment is required. If necessary, more points will be added until more than 2/3 are B or better (B, B+, A- and A).

In any semester at least 2/3 of students will get B or better, and all students in this class can certainly get B or better if we work hard enough to improve both teaching and learning.

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 new textbook was 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.