Suggestions for Instructors

Order of Materials

Materials are presented here in an order appropriate for an upper level undergraduate course in Quantum Mechanics.

The activities in this sequence are meant to draw from standard prerequisites to such a course, such as pendulum motion and wave motion on a string. Review activities on eigenvalues (using pendulum motion) and standing waves on strings might be used individually with students not yet prepared for quantum mechanics.

In addition, while the mathematics involved in the solution to Schrodinger's equation can be difficult even for a problem which has a solution, such as the Hydrogen atom, the solution to the radial problem may prove the easier of the two to introduce to students in a numerical manner, particularly in that the boundary conditions are more physically intuitive. It may be useful for some classes to skip the angular solution, and simply use the known solution for the purposes of visualization.

Introducing students to eigenvalue problems in physics

It should be stressed to the students the meaning of an eigenvalue problem as typically used in physics. While there are mathematically rigorous definitions of the problem in terms of matrix operations, in science it is often used more loosely to describe problems for which there are some finite number of possible solutions that satisfy either boundary conditions or other constraints. It is often described to the student that the particle exists in a superposition of all solutions of Schrodinger's equation, but we do not accept any solution, but rather those that satisfy reasonable boundary conditions. We enforce that a particle bound within some potential be less likely to be found as we move into regions of higher potential. We enforce that the electron's most likely position should not be in the nucleus. Those specific solutions that meet these criteria are the solutions we keep. It should also be stressed to students that there is no single foolproof method for finding eigenvalues, and that they should be prepared to address these problems with a variety of techniques.