PHY 4604 Introductory Quantum Mechanics 1 — Spring 2013
| Class Meetings | Monday, Wednesday, Friday period 6 (12:50–1:40 p.m.) in NPB 1011 |
| Instructor | Prof. Kevin Ingersent, NPB 2162 (392-8748, ingersent@ufl.edu) |
| Office Hours | Mon, Wed, Fri 11:00 a.m.–noon; Tue, Thu 2:00–3:00 p.m.; or by appointment |
| Web Page | www.phys.ufl.edu/~kevin/teaching/4604/ |
| Required Text | Introduction to Quantum Mechanics, D. J. Griffiths (2nd ed., Pearson Prentice Hall, 2005) |
Summary: PHY 4604 is the first course of the two-semester introductory quantum mechanics sequence PHY 4604–4605. The course introduces the basic concepts of wave mechanics, the formalism of quantum mechanics, and applications to atomic, molecular, and condensed matter physics.
Aim: On completion of this course, you should have a sound understanding of key concepts in quantum mechanics, and be able to apply this understanding to analyze, and make both qualitative and quantitative predictions about, the physics of unfamiliar situations. The course should also improve your problem-solving skills.
Prerequisites: You should have successfully completed a college-level course in modern physics at the level of PHY 3101 Introduction to Modern Physics or PHY 3063 Enriched Modern Physics. You should also have passed MAP 2302 Elementary Differential Equations. If you are in doubt as to whether you should take PHY 4604, please consult the instructor as soon as possible.
Text: You will need access to the course text to supplement the lectures, to complete reading assignments and as a source of practice problems. However, you do not necessarily need to purchase your own individual copy.
Griffiths is a good introductory quantum mechanics text. However, you may well wish to consult other texts to get alternative explanations of the course material. Three books in particular are worth considering:
- Principles of Quantum Mechanics by R. Shankar (2nd ed., Springer, 1994). Suitable for advanced undergraduate/beginning graduate study, this book places greater emphasis on the more abstract Dirac formalism in place of wave mechanics. Used as the main text for UF's first-year graduate quantum mechanics courses.
- Quantum Mechanics: A Modern Development by L. E. Ballentine (2nd ed., World Scientific, 1998). Ballentine provides a much more careful discussion of the mathematical underpinnings of quantum mechanics than is usual in standard texts, as well as a passionate exposition of the ensemble interpretation of the state function. A relatively inexpensive paperback, this text is also available as an e-book through the UF library system.
- Physlet Quantum Physics: An Interactive Introduction by M. Belloni, W. Christian, and A. J. Cox (Pearson Prentice Hall, 2006). Contains more than 200 interactive exercises implemented as Java applets, provided on a CD. About two-thirds of the exercises overlap with topics covered in PHY 4604–4605; the rest deal with other aspects of modern physics (such as special relativity and wave-particle duality). The exercises guide the user to adjust applet inputs and interpret the output, which is mostly graphical and in many cases animated. This approach frees one from a lot of cumbersome mathematics to develop intuition about the quantum-mechanical world. This book is also relatively inexpensive.
Homework: Problem solving is integral to mastering any area of physics. For this reason, there will be a homework assignment roughly every two weeks. You will also be recommended to attempt other problems from the text. You should make a good-faith attempt to tackle the problems on your own, but do not spend an inordinate amount of time on any one problem. 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 you are required to write up your own final solution, and you must 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 your sources or copying of some else's solutions are acts of academic misconduct.
Each of the eight homework assignments will have the same maximum number of points available. The sum of your best six homework scores will make up 40% of your overall score on PHY 4604. This weighting is designed in part to encourage you to keep up with the course. For this reason, assignments turned in late will be subject to a significant penalty. Homework will normally be due at the start of a class. The score will be reduced by 25% for work submitted after the due deadline but no later than the start of the first class after the due date. After that, a 50% deduction will apply. No credit will be awarded for homework submitted after the solution has been distributed to the class.
Note that you may turn in for full credit any question parts that you have completed before the 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.
Since only six of eight homework scores contribute to your grade, you can skip two assignments without penalty. You are advised to keep these "free drops" in reserve, in case of some unforeseen eventuality (such as illness) late in the semester. No makeups will be offered for students who miss or are late on three or more assignments.
Exams: There will be three 2-hour exams—two mid-terms held on weekday evenings and a final on Tuesday, May 1; see "Schedule" below for details. The exams will emphasize application of physical concepts to solve problems rather than recalling memorized facts or reproducing standard results. The understanding and skills necessary for success on the exams will be developed by steady work over the entire semester, not by last-minute cramming. You will be allowed to use a formula sheet for each exam, and a calculator at the instructor's discretion, but no other aids will be permitted.
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 distributed in class and posted online.
Grades: The maximum possible total score on the homework assignments will be scaled to 200. Each of the three exams will carry a maximum possible score of 100. Letter grades will be assigned on the basis of the overall course score out of 500. 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. Grades will be assigned in accordance with the University's grading policies.
Attendance Policy: Attendance at lectures is strongly recommended. Material not contained in the textbook will be presented and, in some cases, tested in homework and/or exams. Even if you miss a lecture, you are responsible for staying informed of the material covered and any announcements made in class. Important announcements will also be posted online, and may be accessed by following the Announcements link from the course Web page.
Any request for a special exam sitting or a make-up must be made at least a week ahead for any scheduled absence, and as soon as reasonably possible after an unforeseen absence.
How to Succeed in PHY 4604: 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 the text and the prior-year exams that can be accessed through the course Resources page. Your grade in this course will be based solely on your success at solving problems during homework assignments 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 4604, don't wait to seek help. The course content is largely cumulative, so 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, feel free to contact the instructor to set up an appointment at a more convenient time.
Accommodations: Students requesting classroom accommodations must first register with the Disabilities Resources Center, 0020 Reid Hall. The Disabilities Resources Center will provide documentation to the student, who must then deliver this documentation to the instructor when requesting accommodations.
Academic Honesty: All University of Florida students are required to abide by the University's Academic Honesty Guidelines and by the Honor Code, which reads as follows:
We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: "On my honor, I have neither given nor received unauthorized aid in doing this assignment."
Cheating, plagiarism, or other violations of the Academic Honesty Guidelines will not be tolerated and will be pursued through the University's adjudication procedures.
Schedule: The schedule below lists (1) the topics planned for each lecture, cross-referenced to the text, (2) the planned due-date of each homework assignment, and (3) the date and time of each exam. (The dates of the two mid-terms are tentative.) It is your responsibility to be aware of any changes announced in class. Important announcements will also be posted on the course Web pages.
| Jan 7 | The Schrödinger equation (Secs. 1.1, 1.2) |
| Jan 9 | Probability current (Sec. 1.4, Prob. 1.14). Expectation values (Secs. 1.2, 1.5) |
| Jan 11 | Expectation values (continued). The uncertainty principle (Sec. 1.6) |
| Jan 14 | Stationary states (Sec. 2.1) |
| Jan 16 | The infinite square well (Sec. 2.2) |
| Jan 18 | HW 1 due |
| The infinite square well (continued) | |
| Jan 21 | No class (Martin Luther King, Jr. Day) |
| Jan 23 | The harmonic oscillator (Sec 2.3) |
| Jan 25 | The harmonic oscillator (continued) |
| Jan 28 | The harmonic oscillator (continued) |
| Jan 30 | The free particle (Sec 2.4) |
| Feb 1 | HW 2 due |
| The free particle (continued) | |
| Feb 4 | Boundary conditions on wave functions (Sec 2.5) |
| Feb 6 | The step potential (Prob. 2.34) |
| Feb 8 | The step potential (continued) |
| Feb 11 | The rectangular barrier (Prob. 2.33) |
| Feb 13 | HW 3 due |
| Delta-function potentials (Sec. 2.5) | |
| Feb 15 | The finite square well (Sec. 2.6) |
| Feb 18 | Catch-up/Review |
| Mid-Term Exam: 8:20–10:10 p.m. in NPB 1101 | |
| Feb 20 | Vector spaces (Secs. 3.1, A.1) |
| Feb 22 | Inner products (Secs. 3.1, 3.6, A.2) |
| Feb 25 | Operators (Secs. 3.6, A.3) |
| Feb 27 | Operators (continued). Eigenstates (Secs. 3.3, A.5, A.6) |
| Mar 1 | HW 4 due |
| Eigenstates (continued) | |
| March 4–8 | No class (Spring Break) |
| Mar 11 | The postulates of quantum mechanics (Sec. 3.4) |
| Mar 13 | The postulates of quantum mechanics (continued). The uncertainty principle (Sec. 3.5) |
| Mar 15 | The uncertainty principle (continued) |
| Mar 18 | Quantum mechanics in three dimensions (Sec. 4.1). Spherically symmetric potentials (Sec. 4.1) |
| Mar 20 | Spherically symmetric potentials (continued) |
| Mar 22 | HW 5 due |
| Piecewise-constant spherical potentials (Sec. 4.1) | |
| Mar 25 | The hydrogen atom (Sec. 4.2) |
| Mar 27 | The hydrogen atom (continued) |
| Mar 29 | The hydrogen atom (continued) |
| Apr 1 | Angular momentum (Sec. 4.3) |
| Apr 3 | Angular momentum (continued) |
| Apr 5 | HW 6 due |
| Spin (Sec. 4.4) | |
| Apr 8 | Catch-up/Review |
| Mid-Term Exam: 8:20–10:10 p.m. in NPB 1101 | |
| Apr 10 | Spin (continued) |
| Apr 12 | Spin in a magnetic field (Sec. 4.4.2) |
| Apr 15 | Addition of angular momentum (Sec. 4.4.3) |
| Apr 17 | Addition of angular momentum (continued) |
| Apr 19 | HW 7 due |
| Two-particle systems (Sec. 5.1) | |
| Apr 22 | Two identical particles (Sec. 5.1) |
| Apr 24 | HW 8 due |
| Two identical particles (continued) | |
| Apr 30 | Final Exam: 10:00–noon in NPB 1011 |