Table of Contents
Course Overview
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 two-body 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 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. (more...)
Textbook and Instructor's Guide
Paradigms in Physics: Quantum Mechanics—-a textbook that follows the paradigms approach. The chapters that are relevant to the Central Forces course are:
