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Last Update: 2/16/08 |
Welcome to PH427/527: Periodic Systems. This 3-week module introduces the fundamentals of periodic motion in the context of classical and quantum systems. Such knowledge forms the basis of the theory of solid state physics, the emerging science of photonics, and has relevance to circuit theory, and many engineering applications. The familiar laws of continuum mechanics can be obtained from the limit of the laws pertaining to periodic systems. Since so much of physics is now concerned with matter on an atomic level, it is ever more important to understand the behavior of matter with discrete components.
The classical system is that of beads on a string: we solve Newton's law to find the equations of motion and the dispersion relation for a number of identical beads, and also for a periodic system with two different beads per unit cell. We explore the relevance of this problem to the calculation of the specific heat of a 1-dimensional lattice of atoms, and discuss the concept of phonons. Along the way, we'll be introduced to the concept of the density of states, and we will discuss distribution functions.
The quantum approach considers the solution of Schrödinger's equation in a square well potential that is repeated many times. We discuss the Bloch theorem, which allows us to relate the solution for a single well to the periodic system. We obtain qualitative solutions for the wavefunctions and obtain the dispersion relation that gives the band structure. We apply this to the semiconductor system and calculate carrier densities. Again we'll encounter the density of states concept and distribution functions.
In all cases, we'll use 1-dimensional examples and perform simulations on computers in class. Later, we'll talk about 3 dimensions when we study applications of these ideas.
Hints for success in this class:
· Rule #1: If in doubt, ASK!
· Rule #2: Read the assigned material before class, come to class and do the homework (this gives you a chance to practice Rule #1)
· Rule #3: Seek out the instructors after class (again to put Rule # 1 into practice)
Instruction:
Professor
William Warren
Weniger
313, phone 737-4024, email: wwarren@physics.oregonstate.edu
Office Hours: T 10-11, W
11-12, Th 2-3 and by appointment.
Teaching Assistant:
Jared Stenson
email: stensoja@onid.orst.edu
Office hours: TBA
Meeting Times:
Mondays, Wednesdays and
Fridays at 1:00 pm to 1:50 pm
Tuesdays and Thursdays: 12:00 pm to 1:50 pm
Our class spans the normal lunch hour (especially on T - Th), but please do not each lunch in class as this is very distracting to all concerned, and a danger to the computers. There should be no food or drink in Wngr 304. If you have health constraints such as a diabetic condition, please let me know.
Add/drop and withdrawal dates:
The last day to add/drop this class is the Wednesday of the first week of class. The last day to withdraw is Friday of the second week. See also the link from the paradigms home page that concerns add/drops and withdrawals.
Prerequisites:
You should have taken PH211, 212, 213 and PH314, and the pre- and co-requisite math courses. If you have missed any of the preceding Paradigms, please see the instructor.
Texts:
There are 3 primary texts, and I will supplement with notes. I have listed several references here.
The required text is:
Main, Iain G.,
Vibrations and Waves in Physics, 3/e, Cambridge University Press, 1993.
Supplementary texts are:
Marion J. B., and
Liboff, R., Introductory
Quantum Mechanics 3/e, Addison Wesley, 1998. ISBN 0-201-87879-8 (also used for 1-D Waves, Quantum
Measurements, Central Forces, and Capstone in Quantum Mechanics)
Web page:
The class web page is http://www.physics.oregonstate.edu/ph427 and the syllabus, this document, and several other important pieces of information are there.
Homework:
There will be 3 homework assignments, due on the Friday of each week at the start of class. They are posted in pdf format on the class web page. If you have not completed all problems, turn in what you have done. Late partial assignments may be considered for partial credit at the instructor's discretion. This policy is intended to allow for special situations that can arise. If I detect a pattern of late homework submission, the penalties will increase. The solutions will be posted promptly. Because of the pace of this course, please don't wait for me to return your homework before you go over the posted solutions. Keep a copy of your solutions to compare to the posted ones. Come and ask questions as soon as you can.
I reproduce, for emphasis, the ground rules
laid out in previous paradigm courses:
Ground Rules for Homework:
1. We strongly encourage students to work with each other, more advanced students, the TA, and the professor. However, each student is expected to turn in independent assignments that show evidence of individual thought. This applies most especially to computer assignments. NEVER work together so closely with someone that you produce the same Maple worksheet. This invariably means that one person has been the dominant partner and it is impossible for the instructor to determine who it was. Such assignments will be returned ungraded, and students requested to turn in a new assignment different from each other and different from the original -- probably with a grading penalty added.
Some students find it difficult to decide what constitutes too much collaboration.
(i) Under no circumstances may you ever copy another student's work, even if the two of you have collaborated to work through the problem. Under no circumstances may you ever allow your own work to be copied.
(ii) Try to make progress on a problem on your own. If you cannot, seek help from other resources to overcome a specific hurdle, then try to make further headway on your own. Once you have solved the problem, be honest with yourself about how much intellectual input came from you, and try to improve next time. Rewrite the problem solution without reference to any notes, explaining the steps as you go, as you would to a novice problem solver. Once you have done this, you will have generated a unique solution and one that will have taught you something about what you really understand. Do not be discouraged if you find that some problems require hints and help all the way through. If you are able to explain previously solved problems coherently, you are making good progress.
(iii) A good test of your understanding is to explain a problem to someone else. Be conscious of your role in a collaboration. If it is clear that you have mastered the problem and your collaborator is a novice, limit your help to put the person on the track to solving the problem alone. Do not give too much help. Conversely, if you are seeking help from an expert, don't allow the expert to guide you all the way through. If the exchange is between people of a similar level of understanding, keep challenging one another, asking questions and providing answers, going beyond the limits of the problem. This is the fun part of physics - endless discussion about interesting problems! (Please note that I do not mean to categorize students as "weak or strong". Expert and novice can refer to two students of equal talent and ability - but one happens to have already solved the problem!)
2. Homework solutions from previous years are strictly off-limits. You are on your honor not to use them. Allow faculty to use their time interacting with you, rather than continually thinking up new assignments. Besides, if you don't do the work yourself, it will show up very clearly on exams.
3. Sources must be appropriately documented. If you find a homework problem worked out somewhere (other than homework solutions from previous years), you may certainly use that resource, just make sure you reference it properly. If someone else helps you solve a problem, reference that too. In a research paper, the appropriate reference would be:
Jane Doe, (private communication).
4. If you find that you have worked on a problem for 1/2 hour without making any progress, it would be a good idea to stop and seek help.
"Journal Club" assignment:
You are to read one peer-reviewed journal article on a topic related to the class material. You should write a 3-4 page summary of the paper, which will be due on the last Friday of the class. The material in the paper will (I hope!) be somewhat above the level of what you have learned in the class, so you will have to do some extra work to understand it. Explain what was interesting and why, and outline the extra things you needed to learn to understand the article. I have provided a few examples in this link from which you may choose. I would rather you chose a different article.
Please discuss your choice with me before you begin the writing!
Computer Laboratory:
Much of your learning will be done using computer simulations. Your labs are not turned in or graded, but they are an essential part of your course. Material from the labs is often included on the final exam. Keep good notes as you work.
Final Exam:
There will be a final exam on Monday, April 21 at 19:00 - 20:50 P.M. in Weniger 300 and 304F. This exam will be a closed book exam, but during the course, you, as a group, will be responsible for preparing a single page of notes to bring to the exam. The whole class must have the same page, so it is important for you to compile this sheet in a timely fashion. Think about it as the course progresses.
Course grades:
Homework 30%; Journal Club Paper 20%; Final 50%.
Students with Disabilities:
Students with documented disabilities who may need accommodations, who have any emergency medical information the instructor should know of, or who need special arrangements in the event of evacuation, should make an appointment with the instructor as early as possible, no later than the second day of the class.
If you have comments or suggestions, email me at wwarren@physics.oregonstate.edu
© William W. Warren, Jr., Department of Physics, Oregon State University, 2008