PHY 6646 Quantum Mechanics 2 — Spring 2023

Instructor    Prof. Kevin Ingersent, NPB 2162, 392-8748,
Class Meetings    Mon, Wed, Fri period 4 (10:40–11:30 a.m.) in NPB 1101
Office Hours Mon, Wed, Fri 11:35 a.m.–12:00 p.m.; Tue, Thu 1:00–2:00 p.m.; or by appointment. See Canvas "Announcements" for any office hour changes
Canvas Course Site Login at
Course Prerequisites PHY 6645
Required Text   Principles of Quantum Mechanics, R. Shankar (2nd ed., 1994). Originally published by Plenum Press (ISBN-10: 0306447908). Currently available from Springer as a hardback (ISBN-13: 9780306447907) or an e-book (ISBN-13: 9781475705768).

Summary: PHY 6646 is the second of two courses constituting the graduate core sequence in quantum mechanics. Its aim is to provide a solid grounding in important applications of nonrelativistic quantum mechanics, including approximation methods, scattering theory, and many-particle systems.

Prerequisites: It will be assumed that you have successfully completed (1) at least one year of quantum mechanics at the undergraduate level, and (2) PHY 6645 Quantum Mechanics 1 or equivalent. If you have any doubt about your preparation, you should consult the instructor as early as possible in the semester.

Required Text: Principles of Quantum Mechanics, R. Shankar (2nd ed., Plenum Press, 1994). You do not necessarily need to purchase your own individual copy of Shankar, but you will need access to the book to supplement the lectures, to complete reading assignments, and as a source of problems. The course will generally follow the approach used in Shankar's book, which many readers find to be very helpful in learning the subject. The main ideas are laid out clearly and logically. In places, however, the text stops short of the level of rigor or detail appropriate for a graduate course, so supplementary material will be presented in the lectures. At these points the recommended texts below may prove particularly useful.

Recommended Texts: PHY 6646 will be defined by material covered in class plus readings from Shankar. However, you may wish to consult other sources to see alternative explanations of course topics. Here are three books that are worth considering:

Course Policies

Attendance: Attendance is required only for scheduled exams. Attendance at other class meetings is strongly recommended. Material not contained in the textbook will be presented and, in some cases, tested in homework and/or exams. Past experience indicates that students who do not regularly come to class generally perform poorly on exams and achieve low course grades. If you miss a class, you are responsible for staying informed of the material covered and any announcements made. The Canvas course site (see below) should help with this.

If you are sick, do not come to class. Call your primary care provider if you are ill and need immediate care, or the Student Health Care Center at 352-392-1161 to be evaluated. If you feel well enough to study from home, you can use the Canvas course site and make appointments with the instructor for Zoom meetings to keep up with PHY 6646 until you are able to resume attendance.

Requests for extension of homework deadlines or excused absence from exams will be handled in accordance with UF's attendance policies, and in most cases will require written documentation from an appropriate professional. Any request for a special exam sitting or for a make-up must be made at least seven days ahead for any scheduled absence, and as soon as reasonably possible for an unforeseen absence. If your absence is excused, you will be given a reasonable amount of time to make up missed work.

Canvas Course Site: Course announcements, homework sets and practice exams, solutions to assessments, and grades will be posted on the Canvas course site. You can set your Canvas preferences to receive email notification of each new course announcement.

Course Communication: The preferred method of electronic communication with the instructor is email from a student's Gatorlink account. Canvas Conversations are also an acceptable means of communication. The instructor will endeavor to respond to messages arriving via one of these two routes within one business day. (For example, a message arriving at 4 p.m. on a Friday will normally receive a response by 4 p.m. the following Monday, unless Friday or Monday is a UF holiday.) The instructor will not send course-related correspondence to students at email addresses outside the domain.

Course Demeanor: It is expected that everyone in this class (the instructor and students) will treat one another with dignity and respect, and will follow rules of common courtesy in all course-related interactions, whether online or face-to-face. UF's Netiquette Guide for Online Courses contains valuable advice for conducting electronic communications. Please refrain from actions (including, but not limited to, intrusive use of electronic devices) that distract others in the classroom.

Homework: Problem solving is integral to mastering any area of physics. Most weeks you will be assigned homework due the following week, usually at 5 p.m. on Friday. The sum of your homework scores will make up 40% of your overall score on PHY 6646. Graded homework will be returned in class or during office hours. Homework solutions will be posted in Canvas.

Although the homework is graded, it is intended more as a learning tool than as a means of assessment. To gain maximum benefit, you should make a good-faith attempt to tackle each problem on your own. However, do not spend an inordinate amount of time on any one question. If you get stuck, feel free to discuss your conceptual or technical difficulties with other students or with the instructor. Constructive collaboration is encouraged, but on any assignment submitted for credit, you are required to write up your own final solution and clearly list the names of any and all collaborators and/or solution sources. Providing such a list will not reduce your grade in any way, whereas failure to acknowledge help or copying someone else's work will be treated as an academic honesty violation.

Your submitted homework solutions should explain your reasoning clearly but concisely, cite the source of any results given without proof, and be legible and reasonably neat. Deficiencies in any of these areas may result in deductions from the score you receive Please note that you will receive credit, not for what you know, but rather for what you demonstrate you know by writing it in your solution.

Homework should be submitted on paper (not electronically) and handed to the instructor either in NPB 1101 immediately before/after class or in NPB 2162 at any time when the instructor is present. The instructor will endeavor to be in his office for at least the last couple of hours before the 5 p.m. due deadline for each assignment. He cannot be responsible for the possible loss of work that is not handed directly to him.

Since it is very important that you not fall behind in the course, the score will be reduced by 25% for homework submitted after the due deadline but before the final cut-off announced for the assignment. You may turn in for full credit any question parts that you have completed by the due deadline, and later submit additional work for partial credit. However, only the first submitted version of each separate question part [e.g., question 2(c)] will be graded. Each student will receive a waiver of the 25% late penalty for one assignment during the semester.

The homework will be graded by a graduate teaching assistant, under the supervision of the instructor. The grader will have some discretion in the assignment of scores, subject to the guiding principles of accuracy (the score awarded for each answer reasonably reflects the progress made towards a complete, correct solution) and consistency (all students submitting equivalent answers receive the same score). If you have any questions or concerns about the score you receive on a homework assignment, please contact the instructor. You should not discuss the homework problems or their grading with the grader.

Exams: There will be three exams—two 110-minute mid-terms held on weekday evenings and a 120-minute final on May 2; see "Schedule" below for details. Each exam will count 20% toward your final course grade. Graded exams will be returned in class or during office hours. Exam solutions will be posted in Canvas.

Approximately half of each exam will be closely related to homework. However, the questions will not merely require memorization and regurgitation of material covered in lectures and homework. Instead, the emphasis will be on application of concepts and methods to fairly straightforward problems, some of which may deal with unfamiliar situations. You may be allowed limited access to written materials (details will be announced before each exam), but no collaboration will be permitted.

Grades: Letter grades will be assigned in accordance with the University's grading policies on the basis of an overall course score constructed as follows:

Sum of homework scores 40%
Exam 1 20%
Exam 2 20%
Final exam 20%

There is no rigid point scale or grade curve used to assign letter grades for the course. Grades of "A", "A-", and "B+" reflect performance at the level expected of Ph.D. candidates, while a "B" grade indicates attainment at the master's level. Guidance as to the likely scale used to convert course scores to letter grades will be provided after each mid-term exam and before the final exam.

Student Complaints Process: Please discuss any concern about the course with the course instructor. If this doesn't lead to a satisfactory resolution, students should contact Department of Physics Chair Prof. Stephen Hagen or the UF Office of the Ombuds.

Schedule: The schedule below lists (1) the general topic(s) planned for each lecture, (2) the planned due-date of each homework assignment, and (3) the date, time, and location of each exam (updated on January 20 with the Registrar's scheduling of the two mid-terms). It is your responsibility to be aware of any changes announced in class. Important announcements will also be posted on the course Canvas pages.

Week 1 Mon Jan 9 First class
Wed Jan 11 Spin (continued)
Fri Jan 13 Spin (continued)
Week 2 Mon Jan 16 No class: Martin Luther King Jr. Day
Wed Jan 18 Addition of angular momentum
Fri Jan 20 Addition of angular momentum (continued)
Homework 1: due at 5 p.m.
Week 3 Mon Jan 23 Addition of angular momentum (continued)
Wed Jan 25 Addition of angular momentum (continued)
Fri Jan 27 Charged particle in an electromagnetic field
Week 4 Mon Jan 30 Charged particle in an electromagnetic field (continued)
Wed Feb 1 Charged particle in an electromagnetic field (continued)
Fri Feb 3 Charged particle in an electromagnetic field (continued)
Homework 2: due at 5 p.m.
Week 5 Mon Feb 6 Charged particle in an electromagnetic field (continued)
Wed Feb 8 Charged particle in an electromagnetic field (continued)
Fri Feb 10 Charged particle in an electromagnetic field (continued)
Homework 3: due at 5 p.m.
Week 6 Mon Feb 13 Variational method
Wed Feb 15 Variational method (continued)
Fri Feb 17 Variational method (continued)
WKB method
Homework 4: due at 5 p.m.
Week 7 Mon Feb 20 WKB method (continued)
Wed Feb 22 WKB method (continued)
Exam 1: 8:20–10:10 p.m. in NPB 1101
Fri Feb 24 WKB method (continued)
Week 8 Mon Feb 27 Time-independent perturbations
Wed Mar 1 Time-independent perturbations (continued)
Fri Mar 3 Time-independent perturbations (continued)
Homework 5: due at 5 p.m.
Week 9 Mon Mar 6 Time-independent perturbations (continued)
Wed Mar 8 Time-independent perturbations (continued)
Fri Mar 10 Time-dependent perturbations
Homework 6: due at 5 p.m.
Week 10 Mon Mar 13 No class: Spring Break
Wed Mar 15 No class: Spring Break
Fri Mar 17 No class: Spring Break
Week 11 Mon Mar 20 Time-dependent perturbations (continued)
Wed Mar 22 Time-dependent perturbations (continued)
Fri Mar 24 Time-dependent perturbations (continued)
Homework 7: due at 5 p.m.
Week 12 Mon Mar 27 Time-dependent perturbations (continued)
Wed Mar 29 Time-dependent perturbations (continued)
Fri Mar 31 Time-dependent perturbations (continued)
Homework 8: due at 5 p.m.
Week 13 Mon Apr 3 Scattering
Wed Apr 5 Scattering (continued)
Thu Apr 6 Exam 2: 8:20–10:10 p.m. in NPB 1101
Fri Apr 7 Scattering (continued)
Week 14 Mon Apr 10 Scattering (continued)
Wed Apr 12 Scattering (continued)
Fri Apr 14 Scattering (continued)
Homework 9: due at 5 p.m.
Week 15 Mon Apr 17 Identical particles
Wed Apr 19 Identical particles (continued)
Fri Apr 21 Identical particles (continued)
Homework 10: due at 5 p.m.
Week 16 Mon Apr 24 Relativistic quantum mechanics
Wed Apr 26 Last class
Relativistic quantum mechanics (continued)
Fri Apr 28 Homework 11: due at 5 p.m.
Week 17 Tue May 2 Final Exam: 3:00–5:00 p.m. in NPB 1101

Disclaimer: This syllabus represents the instructor's current plans and objectives. As we go through the semester, those plans may need to change. Such changes, communicated clearly, are not unusual and should be expected.

University Policies

Accommodating Students With Disabilities: Students with disabilities who experience learning barriers and would like to request academic accommodations should connect with the Disability Resource Center. It is important for students to share their accommodation letter with the course instructor and discuss their access needs as early as possible in the semester because accommodations are not retroactive.

In-Class Recording: Students are allowed to record video or audio of class lectures. However, the purposes for which these recordings may be used are strictly controlled. The only allowable purposes are (1) for personal educational use, (2) in connection with a complaint to the university, or (3) as evidence in, or in preparation for, a criminal or civil proceeding. All other purposes are prohibited. Specifically, students may not publish recorded lectures without the written consent of the instructor.

A "class lecture" is an educational presentation intended to inform or teach enrolled students about a particular subject, including any instructor-led discussions that form part of the presentation, and delivered by any instructor hired or appointed by the University, or by a guest instructor, as part of a University of Florida course. A class lecture does not include lab sessions, student presentations, clinical presentations such as patient history, academic exercises involving solely student participation, assessments (quizzes, tests, exams), field trips, private conversations between students in the class or between a student and the faculty or lecturer during a class session.

Publication without permission of the instructor is prohibited. To "publish" means to share, transmit, circulate, distribute, or provide access to a recording, regardless of format or medium, to another person (or persons), including but not limited to another student within the same class section. Additionally, a recording, or transcript of a recording, is considered published if it is posted on or uploaded to, in whole or in part, any media platform, including but not limited to social media, book, magazine, newspaper, leaflet, or third party note/tutoring services. A student who publishes a recording without written consent may be subject to a civil cause of action instituted by a person injured by the publication and/or discipline under UF Regulation 4.040 Student Honor Code and Student Conduct Code.

Honor Code: UF students are bound by The Honor Pledge: "We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: The Student Conduct Code specifies a number of behaviors that are in violation of this code and the possible sanctions. Furthermore, you are obligated to report any condition that facilitates academic misconduct to appropriate personnel. If you have any questions or concerns, please consult with the course instructor.

Evaluation: Students are expected to provide professional and respectful feedback on the quality of instruction in this course by completing course evaluations online via GatorEvals. Guidance on how to give feedback in a professional and respectful manner is available at Students will be notified when the evaluation period opens, and can complete evaluations through the email they receive from GatorEvals, in their Canvas course menu under GatorEvals, or via Summaries of course evaluation results are available to students at

How to Succeed in PHY 6646

You should attend class to learn about the basic concepts and how to apply them in solving problems. Arrive on time for class, since announcements will generally be made at the start of each lecture.

It will likely benefit you to read the textbook in advance to acquaint yourself with the material to be covered. This will allow you to focus during the class on the more subtle points.

You should work all the homework assignments, which form an essential part of the course. With all the opportunities to achieve a high score (see "Homework" above), you should look to the homework to establish a strong foundation for your overall course score (see "Grades" above).

Problem solving provides a good measure of your understanding of basic principles by testing your ability to combine different physical concepts as they apply to unfamiliar situations. If you find that you are struggling with the homework, or if you want to improve your performance on the exams, you should practice additional problems beyond the assigned homework. The best sources of practice problems are (1) the text and (2) the prior-year exams that can be accessed through the "Practice Exams" page in the course Canvas site. Your grade in this course will be based solely on your success at solving problems during homework assignments, quizzes, and exams, so there will be a direct payoff for your effort.

You will learn most if you try each problem on your own first. If you get stuck, talk the problem over with a friend, consult the instructor, or check the solution (if one is available). Whenever you need help to complete a problem it is essential, though, that you consolidate your new understanding by successfully doing another problem of the same type by yourself. Don't despair if you seem to make a lot of mistakes at the start. A successful physicist is basically somebody who has made all possible mistakes in the past and has learned how to avoid repeating most of them!

If you are encountering difficulties with PHY 6646, don't wait to seek help. If you fall behind it will be hard to catch up. You are encouraged to consult with the instructor in person or via e-mail. When using e-mail, please make any physics questions as specific as possible, and recognize that it may be some time before you get a reply (especially outside normal business hours). Discussion of complex matters is usually best conducted face to face, either immediately after class or during office hours. If your schedule prevents you from attending office hours, please contact the instructor to set up an appointment at a mutually convenient time.

Getting Help

Campus Resources: See for: