An introduction to quantum physics. We explore the mathematical structure of quantum theory, the notion of superposition, and the idea of quantum entanglement (including the Bell inequalities). Our principal examples are based on spin-1/2 systems, the most basic quantum systems.
It is expected that students will
The textbook for the course is Quantum Processes, Systems, and Information by Benjamin Schumacher and Michael D. Westmoreland, Cambridge University Press, ISBN 978-0-521-87534-9.
There will be three 50-minute exams during the normal class time. There will also be a comprehensive final exam. No computers, cell phones, music players, or any electronic devices with wireless or network capability are allowed during exams. We will discuss whether or not calculators will be needed on exams.
The textbook by Schumacher and Westmoreland contains exercises scattered through the sections and problems at the end of each chapter. I will ask you to read sections of the textbook before coming to class. Please do all of the exercises in each section I assign and bring that work to class. If you cannot complete an exercise, write down a question that helps to uncover where your confusion, misunderstanding, or unawareness lies (or stop by for help). I may or may not collect the daily exercises. The daily exercises will be graded primarily on effort, and will count toward your homework grade for the class.
In addition to the daily exercises, there will be problem sets that are due from time to time. The due dates for the problem sets are listed below. The problem sets will be graded primarily on results (as opposed to effort), and will count toward your homework grade for the class.
You may work together on the daily exercises and on the problems sets, talking about how to solve the problems, but you must write your solutions independently. Do not copy homework solutions from your classmates or from any other source. Copying another person’s homework solutions is an act of cheating and plagiarism. Submitting your own work for the homework will cause you to learn quantum theory. Everything that you write in your homework solutions you should be able to explain to me if I ask. This does not mean that your homework needs to be perfect, only that it must have come from your mind.
If you can’t finish some of the problems before the due date, turn in what you have done. It is still worth trying to do the remaining problems, because they all have a purpose in learning quantum theory. If you know in advance that you will have trouble finishing the homework by the deadline, come and talk to me.
A portion of your grade is determined by class participation. Obviously, attendance is a prerequisite for participation in class. If you attend every class, and participate by asking questions, answering questions, and taking your turn in doing problems at the board, you will have a perfect score for this area. If you need to miss a class, see me in advance if you can, and turn in a written copy of the daily exercises we planned to discuss that day.
Your grade will be determined by a weighted average as indicated in the table below.
| Exams | 45% |
| Homework | 30% |
| Class Participation | 10% |
| Final Exam (comprehensive) | 15% |
Your letter grade for the course is determined by the weighted average. The minimum weighted average (out of 100) required for each letter grade is indicated below.
| A | 93 |
| A- | 90 |
| B+ | 87 |
| B | 83 |
| B- | 80 |
| C+ | 77 |
| C | 73 |
| C- | 70 |
| D+ | 67 |
| D | 63 |
| D- | 60 |
| F | 0 |
Please feel free to stop by my office any time to chat. I will make a special effort to be in my office during the office hours posted on my door (also listed on my web page). We can also make an appointment to get together if that is convenient for you.
If you have a physical, medical, psychological, or learning disability that is going to impact your attendance or require accommodation, please let me know. In order to ensure that your learning needs are appropriately met, you will need to provide documentation of your disability or medical condition to the Director of Disability Services. The Office of Disability Services will then provide a letter of verification of disability that describes the accommodations needed for this class. This office is located in the Humanities Building, room 04, and the Director may be reached by phone at 717-867-6071.
Lebanon Valley College’s Academic Honesty Policy is written in the college Catalog, and at http://www.lvc.edu/catalog/acad-reg-procedures.aspx. This code asks each student to do their own work in their own words:
Lebanon Valley College expects its students to uphold the principles of academic honesty. Violations of these principles will not be tolerated. Students shall neither hinder nor unfairly assist the efforts of other students to complete their work. All individual work that a student produces and submits as a course assignment must be the studentâs own. Cheating and plagiarism are acts of academic dishonesty. Cheating is an act that deceives or defrauds. It includes, but is not limited to, looking at another’s exam or quiz, using unauthorized materials during an exam or quiz, colluding on assignments without the permission or knowledge of the instructor, and furnishing false information for the purpose of receiving special consideration, such as postponement of an exam, essay, quiz, or deadline of an oral presentation. Plagiarism is the act of submitting as oneâs own the work (the words, ideas, images, or compositions) of another person or persons without accurate attribution. Plagiarism can manifest itself in various ways: it can arise from sloppy, inaccurate note-taking; it can emerge as the incomplete or incompetent citation of resources; it can take the form of the wholesale submission of another person’s work as one’s own, whether from an online, oral or printed source. The seriousness of an instance of plagiarism—its moral character as an act of academic dishonesty—normally depends upon the extent to which a student intends to deceive and mislead the reader as to the authorship of the work in question. Initially, the instructor will make this determination.
Once academically dishonest work has been submitted, the instructor shall report the suspected incidence to the associate dean of the faculty. At the moment the work has been submitted, the student involved forfeits the right to withdraw from the course or to change his or her course status in any way. The College’s expectations and the measures it will apply to support and enforce those expectations are outlined below.
For the first offense of academic dishonesty, the faculty member has the option of implementing whatever grade-related penalty he or she deems appropriate, up to and including failure in the course. The associate dean of the faculty shall send the student a letter of warning, explaining the policy regarding further offenses and the appeal process.
| Date | Topic | Read before class | Hand in |
|---|---|---|---|
| 01/18 | Welcome | ||
| 01/20 | Complex numbers | QRGLAQM Sec. 1 | |
| 01/22 | Interferometer | 2.1 (Ex. 2.1–2.10) | |
| — | |||
| 01/25 | Photon | 2.1 (Ex. 2.11–2.17) | PS 1 |
| 01/27 | Spin 1/2 | 2.2 | |
| 01/29 | Bases | ||
| — | |||
| 02/01 | Two-level atoms | 2.3 | |
| 02/03 | Time evolution | PS 2 | |
| 02/05 | Qubits | 2.4 | |
| — | |||
| 02/08 | Ch. 2 summary | ||
| 02/10 | Hilbert space | 3.1 (Ex. 3.1–3.10) | PS 3 |
| 02/12 | Operators | 3.2 (Ex. 3.11–3.20) | |
| — | |||
| 02/15 | Exam 1 (Ch. 2) | ||
| 02/17 | Operators | 3.2 (Ex. 3.21–3.28) | |
| 02/19 | Observables | 3.3 | |
| — | |||
| 02/22 | Adjoints | 3.4 (Ex. 3.34–3.42) | PS 4 |
| 02/24 | Eigenvalues | 3.5 (Ex. 3.43–3.49) | |
| 02/26 | Eigenvectors | 3.5 (Ex. 3.50–3.56) | |
| — | |||
| 02/29 | Distinguishability | 4.1–4.2 | |
| 03/02 | Cryptography | 4.3–4.4 | PS 5 |
| 03/04 | Uncertainty | 4.5 | |
| — | |||
| 03/07 | Spring vacation | ||
| 03/09 | Spring vacation | ||
| 03/11 | Spring vacation | ||
| — | |||
| 03/14 | Evolution | 5.1 | |
| 03/16 | Schrodinger eqn. | 5.2 | |
| 03/18 | Clocks | 5.3, 5.4 (Ex. 5.12–5.16) | |
| — | |||
| 03/21 | Symmetries | 5.4 (Ex. 5.17–5.22) | |
| 03/23 | Composite systems | 6.1 (Ex. 6.1–6.6) | PS 6 |
| 03/25 | Easter vacation | ||
| — | |||
| 03/28 | Easter vacation | ||
| 03/30 | Composite systems | 6.1 (Ex. 6.7–6.11) | |
| 04/01 | Exam 2 (Ch. 3, 4, 5) | ||
| — | |||
| 04/04 | Entanglement | 6.2 | |
| 04/06 | A 4pi world | 6.3 | |
| 04/08 | Conditional states | 6.4 | |
| — | |||
| 04/11 | Bell’s theorem | 6.5, 6.6, 6.7 | PS 7 |
| 04/13 | Particle in space | 10.1 | |
| 04/15 | Continuous observables | 10.2 (Ex. 10.6–10.11) | |
| — | |||
| 04/18 | Wave packets | 10.3, 10.4 | |
| 04/20 | Continuous observables | 10.2 (Ex. 10.12–10.17) | |
| 04/22 | ValleyFest, no class | ||
| — | |||
| 04/25 | More space | 10.5, 10.6 | PS 8 |
| 04/27 | Dynamics in 1-D | 11.1, 11.2 | |
| 04/29 | Exam 3 (Ch. 6, 10) | ||
| — | |||
| 05/02 | Particle in a box | 11.3, 11.4 | |
| 05/04 | Quantum Billiards | 11.5 | PS 9 |