Description & Outcome 
The Central Forces Paradigm presents, in parallel, a classical and quantum mechanical treatment of the problem of two bodies moving under the influence of a mutual central force. The course begins with identifying this central force problem and reformulating the twobody problem in terms of a reduced mass. The classical part of this course asks the students to consider planetary orbits, emphasizing the use of energy and angular momentum conservation and an analysis of the effective potential. The quantum portion of course asks the students to find the analytic solution of the unperturbed hydrogen atom. This solution is built from simpler examples (a particle confined to a ring and a particle confined to a spherical shell) that introduce students to the relevant special functions needed for the full hydrogen atom solution. Another theme developed in this course is the treatment of breaking up problems in several dimensions into problems involving one dimension at a time. In the classical part of the course, students use conserved quantities to break up a vectorvalued ordinary differential equation into its spherical coordinate components. In the quantum part of the course, students use separation of variables to break the partial differential equation (energy eigenvalue equation) up into singlecoordinate eigenvalue equations.
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Times, Dates and Locations 
 Class meets MWF at 13:00  13:50 and TR at 12:00  13:50 from 2/27/2012 to 3/16/2012.
 Class meetings are in WGR 212, 304, 304F, as noted in the syllabus or in class.
 Final exam: see below AddDrop, Withdraw & Final dates.
 This 2credit course meets for 1/3 of the term. The work is thus concentrated and is equivalent to TWO 3credit courses meeting 3 days/week for the full term.
 Instructor & TA office hours are posted on the class web page.
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Class Web page, Email 

Course Evaluation 
 PH426: Homework 50%; Final Exam 50%.
PH526: Homework 40%; Paper 20%; Final Exam 40%.
 Homework: Required problems will be graded. Solutions will be posted online. Assignments turned in after solutions are posted can earn at most 50% of the total points. Very late assignments will earn less. It is a good idea to turn in what you have done by the due date, and, if necessary, the rest later.
 Practice problems provide simple examples for you to check whether or not you understand the material as you go along. They will not be graded. Sometimes solutions will be posted. At a minimum, you should read each practice problem and make sure that you know how to do it. If you can't, ask for help!
 Final exam: The final exam involves problems similar to those encountered in the homework assignments, and the work explored in the physical and computational laboratory experiences. No programming will be required.
 PH 526 requirements: A short paper on a topic of your choosing is required. It should include a brief introduction, a calculation, and some comment on why the calculation is useful or interesting. It can be an extension of some problem assigned in the text or the resources, and should be handed in and presented as a 10minute talk on the final day of class. A topic should be proposed in writing by March 7. The level of effort expected is approximately equivalent to 12 homework assignments.
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Class Participation 
You must be actively engaged in learning in every mode of instruction. In lecture mode, listen actively (it iss not trivial), and ask and respond to questions. In lab mode, question as you perform experiments. Observe carefully. You will often work together in groups in both lecture and lab mode. It is an efficient way to learn, because your peers are a vast source of information, largely untapped in traditional passive learning. It allows the instructor to address issues specific to smaller subsets of the class, while still having the entire class actively engaged. Learn to taken on all roles in a group  leader, questioner, scribe, reporter. You will find these skills are essential in a "real world" scientific environment. Learn actively, and be a good citizen in your group; do not abuse the system. Helping others learn elevates the level of your own learning. But do not rely on others to get you through. It is ALWAYS your responsibility to go over group work alone to ensure that YOU have have understood the information discussed.
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Ground Rules 
Science is inherently a social and collaborative effort, each scientist building on the work of others. Nevertheless, each student must ultimately be responsible for his or her own education. Therefore, you are expected to abide by a number of Ground Rules:
 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. The final synthesis must be entirely your own. This applies also to, and especially to, computergenerated worksheets. NEVER work together so closely with someone that you produce the same solution or Mathematica 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 both (or all) students requested to turn in a new assignment different from each other and different from the original.
 Homework solutions from previous years are very strictly offlimits. You are on your honor not to use them, and not to share your homework solutions with other students. 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 later. Likewise, the solutions provided by the instructors are for your personal use only. You may make one copy and keep it in your personal files.
 Sources must be appropriately documented. If you work with other students in a laboratory assignment, you must write down who your partners were. If you find part of a homework problem worked out somewhere (other than homework solutions from previous years), you may 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).
 Plagiarism  representing someone else's work as your own  is unethical, but collaboration and exchange of ideas is healthy. You can avoid collaborative efforts taking on the look of plagiarism by acknowledging sources and by writing up your work independently.
Some students find it difficult to decide what constitutes too much collaboration. Here are some guidelines:
 Under no circumstances may you ever copy another student's work, even if you have collaborated to work through the problem. Under no circumstances may you ever allow your own work to be copied. Violation of this rule will certainly result in a zero grade for the assignment, and may result in an F grade in the course.
 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.
 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! (There is no intention to categorize students as ÒweakÓ or ÒstrongÓ. Expert and novice can refer to two students of equal talent and ability  but one happens to have already solved the problem!)
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Resources 
The main Paradigms webpage lists all the Paradigms texts, and gives information about the OSU library.
Texts: For PH 426, you will find useful
 (T) Taylor, Classical Mechanics (required, used often)
 (Mc) McIntyre, Quantum Mechanics (required, used often)
 (RHB) Riley, Hobson & Bence, 2nd ed, Mathematical Methods for Physics & Engineering, (mostly reference, alternatives acceptable)
 Your calculusbased introductory Physics text.
Computers: Please see the Paradigms Homepage about computer requirements for the course.
 The class makes use of Mathematica, a computer algebra program. You don't need any experience; familiarity with any programming environment is all that is needed, along with a willingness to learn. The Mathematica page provides more resources.
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Add, Drop, Withdraw & Final Exam Dates 
Special add/drop dates are in effect for the Paradigms courses. Check with the registrar.
The Final exam for PH 426 is Monday, 3/19/2012 at 12:001:50 pm.
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Students with Special Needs 
Students with documented disabilities who may need accommodation, who have any medical information which the instructor should know of, or who need special arrangements in the event of evacuation, should make an appointment to discuss their needs with the instructor as early as possible, and no later than the first week of the term.
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