Physics 426 Spring 2015
This is one of the courses in the Paradigms in Physics series. Please see http://physics.oregonstate.edu/paradigms/index for general information about the program.
Instructor: Oksana Ostroverkhova, oksana@science.oregonstate.edu
Class TA : Rabindra Bajracharaya (bajrachr@onid.orst.edu)
Meeting times: MWF 1-1:50 PM, TR 12-1:50 PM, Weniger 304
Office hours: Weniger 413, WF 2 – 3 PM, or by appointment
TA office hours: Weniger 304F or 491, TR 2-3 PM
Textbooks:
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McIntyre, “Quantum Mechanics: A Paradigms Approach”, 1st edition.
Taylor, “Classical Mechanics” (2005)
Software: Mathematica; free download is available through OSU
(http://my.science.oregonstate.edu/software/mathematica_info)
Pre-requisites: 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. We will build on concepts and mathematical techniques from previous Paradigms as well as the Paradigms Preface week.
Course summary:
The Central Forces Paradigm presents, in sequence, 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.
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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.
The course also uses the paradigmatic example of a central force to introduce students to techniques for dealing with coupled differential equations, in particular breaking up a problem 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 vector-valued 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 (Schrodinger's equation) up into single-coordinate eigenvalue equations.
By the end of the course students should:
 Characterize central forces and identify the similarities and differences between classical and quantum mechanics in the context of central forces.
 Discuss how conserve quantities (energy and angular momentum) constrain a physical system
 Use several methods (including series solutions) to solve ordinary differential equations
 Create a graph of the effective potential for systems with different potentials and use the graph to predict the behavior of the system.
 Use separation of variables to separate a partial differential equation into a set of ordinary differential equations.
 For three different quantum systems: a particle confined to a ring, a particle confined to a spherical shell (rigid rotor), and the hydrogen atom, o Identify the Hamiltonian and energy eigenvalues for the given quantum system, and o calculate probabilities, expectation values, uncertainties, and time evolution for the given quantum system.
 Use special functions to expand a generic quantum state in terms of the eigenfunctions of a complete set of commuting operators.
Homework:
We will have several homework assignments every week. Assignments will be posted on the class webpage. Required homework problems should be submitted by 5 PM on the due date. Solutions will be posted immediately after the deadline. Late homework will not be accepted .
Pay attention to your presentation - clarity, neatness, and logical structure contribute to the overall assessment. Make your solutions a model that a beginning sophomore in physics could work from. Collaboration on homework is encouraged, but write-ups must

be completely and absolutely independent. 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. Practice problems provide simple examples for you to check whether or not you understand the material as we go along. They will not be graded.
Worksheets:
In order to help you check your understanding of the material and provide instantaneous feedback for me, worksheets will be handed out several times a week for in-class work.
Filled out worksheets will be collected, graded, and returned at the next class.
Exam:
The final exam involves problems mostly similar to those encountered in the homework assignments, and in the physical and computational laboratory experiences. (No
Mathematica or other programming will be required). As usual in the Paradigms, the final will be held on the Monday evening following the last day of class, June 8, 7:00 – 8:50
PM.
Grading Policy:
Homework (total) 40%
Worksheets (total) 10%
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.