- Instructor: Wouter Deconinck
- Phone: 757-221-3539
- Email: wdeconinck@wm.edu
- Class location: Small Hall 122
- Class hours: MW 11am-12:20pm
- Office location: Small Hall 343D
- Office hours: you are welcome to stop by my office any time, or make an appointment at http://www.doodle.com/wdeconinck
In this course we will explore an axiomatic development of wave mechanics and the Schroedinger equation in one and three dimensions; wave packets; spin and angular momentum.
- Stern-Gerlach experiment and qubits
- Formal framework of quantum mechanics:
- Hilbert space of states
- Matrix, ket, and functional representations
- Connections with classical mechanics
- Postulates of quantum mechanics
- Symmetries and conservation laws
- Translations
- Parity
- Vector and tensor operators
- Rotations
- Spherical harmonics
- Angular momentum
- Orbital and spin angular momentum
- Addition of angular momentum
- Wigner-Eckart theorem
At the end of this semester you should be able to:
- list and explain the fundamental postulates of quantum mechanics;
- discuss the meaning of the Schroedinger wavefunction;
- relate the mathematical definition and physical meaning of hermitian and unitary operators, respectively;
- recognize and distinguish finite discrete, infinite discrete, and infinite continuous quantum state spaces;
- define what an entangled state is; give an example of such a state;
- explain the connection between the SU(2) and SO(3) symmetry groups;
- write down and contrast the general forms of the translation operator and the rotation operator, and their generators;
- differentiate between the Schroedinger, Heisenberg, and Interaction pictures
Although no single textbook is required, there are a variety of textbooks that can be used in this course. Although the intention is not to adhere closely to either one of them, I will draw on the structure and examples in the following textbooks.
- J. J. Sakurai, Modern Quantum Mechanics (1985). The first two chapters are universally praised for their clarity, but despite its name this is not a very modern treatment of quantum mechanics anymore. In a more recent edition with J. J. Napolitano (2010) a chapter on relativistic quantum mechanics was added.
- M. Le Bellac, Quantum Physics (2012)
- K. Gottfried, T.-M. Yan, Quantum Mechanics: Fundamentals (2003)
- E. Merzbacher, Quantum Mechanics (1998)
It is assumed that you have taken a two semester undergraduate quantum mechanics course, likely based on Introduction to Quantum Mechanics by D. J. Griffiths. You should have completed chapters 1 through 6.
No matter how much the instructor lectures at you, it is my conviction that you will learn more by engaging actively with the material. Quantum mechanics is a tool to master, not a topic to hear and forget about.
In advance of each class you will complete a short assignment (category C: individual assignment but you may work with others). Bring your solution to class as you may be selected to present it. You will not be graded on the correctness of this assignment, but the lack of a good faith effort will affect your participation grade.
In each class session you will work in group on some more advanced problems, some of which may be similar to those on the homework assignments.
The homework assignments (category C, unless otherwise specified) are due at the beginning of Wednesday's lecture. There will be no credit for unexcused delays. Anticipated delays must be communicated to the instructor in a timely fashion to be considered.
The midterm exam will be a take-home assignment (category A). You will have one full week to complete it. The exact week when you will be completing the midterm exam will be decided in coordination with the instructors of other first year graduate courses.
The final exam will be a take-home assignment (category A). You will have one full week to complete it. The final exam will be due at the time when an in-class exam would normally be scheduled by the registrar. There will be no in-class final exam.
Your grade in this course will be based for 20% on your participation in class, for 40% on your homework assignments, for 20% on your midterm exam, and for 20% on your final exam.
As a member of the William and Mary community, I pledge on my honor not to lie, cheat, or steal, either in my academic or personal life. I understand that such acts violate the Honor Code and undermine the community of trust, of which we are all stewards.
Academic integrity is an integral component of William & Mary's learning experience and any breech of this integrity is very serious and not in keeping with the overall intellectual and ethical foundations of our University. Students are expected to adhere to William & Mary's Honor Code and to the general principles of academic honesty. These principles include and incorporate the concept of respect for the intellectual property of others, the expectation that assignments will be submitted according to guidelines specified by the instructor, and that plagiarism of any type is unacceptable.
For this course we will be using assignment categories developed within the Mason School of Business. Every assignment given in this course will be identified by a letter code. We may not use all categories of assignments in this course.
- CATEGORY A: This is an individual assignment. You many not receive help from anyone on this assignment. It must be 100% your own work. All questions concerning this assignment should be addressed to your professor. It is an honor code offense to give or receive assistance on this assignment.
- CATEGORY B: This is a group assignment. Your group may not receive help from anyone outside your group. While your group may choose to delegate the work among the group members, everyone in the group is expected to be prepared to discuss the entire assignment in class. All questions concerning this assignment should be addressed to your professor. It is an honor code offense to give help to other groups and individuals or receive assistance from other groups and individuals.
- CATEGORY C: This is an individual assignment. You may work with others or receive help from a tutor on this assignment. You must, however, turn in your own paper. You may not divide the work with others or copy another student’s paper; it is an honor code offense to do so.
- CATEGORY D: This is a group assignment. You may share information, discuss general concepts and approaches to the assignment with other groups. Everyone in the group should be prepared to discuss the entire assignment in class. Each group must turn in their own work. You may not copy another group’s work; it is an honor code offense to do so.
- CATEGORY E: This is a timed assignment. You are given a specific length of time within which the work must be completed. It is an honor code offense to violate this time restriction unless you have received permission from your professor.
William & Mary accommodates students with disabilities in accordance with federal laws and university policy. Any student who feels they may need an accommodation based on the impact of a learning, psychiatric, physical, or chronic health diagnosis should contact Student Accessibility Services staff at 757-221-2512 or at sas@wm.edu to determine if accommodations are warranted and to obtain an official letter of accommodation. For more information, please visit http://www.wm.edu/sas.
If you feel that there is anything that I, as the instructor, can do to ensure a better learning environment for you, please do not hesitate to contact me. As long as these ad-hoc accommodations do not unfairly disadvantage other students, I am more than willing to help out.
- L. D. Carr, S. B. McKagan, Graduate Quantum Mechanics Reform (2009); arxiv: 0806.2628.
- W&M Student Accessibility Services, Example Syllabus Statement. Retrieved August 30, 2017.
- W&M Mason School of Business, Honor Code Assignment Categories. Retrieved August 30, 2017.
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