Books:

• Quantum Mechanics Using Maple : With 75 Exercises and Cross Platform Diskette Containing 39 Guided Maple Sessions/Book and Disk by Marko Horbatsch. (Springer Verlag ,1995) ISBN: 3540588752

• Quantum Mechanics Using Computer Algebra : Includes Sample Programs for Reduce, Maple, Mathematica and C++ by Willi-Hans Steeb. (World Scientific Publishing Co., 1994) ISBN: 9810217706

• The Picture Book of Quantum Mechanics by Siegmund Brandt and Hans Dieter Dahmen. 2nd Edition (Springer Verlag ,1995) ISBN: 0387943803 . . . . . . very good for ideas for graphs to aid visualization

• Introduction to Quantum Mechanics by David J. Griffiths. (Prentice Hall, 1994) ISBN: 0131244051 This is a widely used upper-level undergraduate text. It has relatively few graphs so it is especially open to help from Maple.

• Quantum Mechanics (Physics and Its Applications) by David S. Betts and Paul C.W. Davies. 2nd Edition (Chapman & Hall, 1994) ISBN: 0412579006 . . . only about 100 pages long.

• Understanding Quantum Mechanics , Morrison - Out of print?? . . . quite excellent because of its good discussion of fundamental concepts.

Web sites:

• http://krupp.claremont.edu/physics/physics114-f96.html

Topics for which Maple should be especially useful:

• 1) Group velocity.
• 2) Shooting technique - a predictor technique for solving differential equations. (predictor/corrector approach). Very good for determining eigenvalues and eigenfunctions.
• 3) Visualization of electromagnetic waves to wave packets, matter waves and their wave packets.
• 4) Operators and commutation relations.
• 5) Stern-Gerlach experiment - can have 3, 5, 7, etc., angular momentum states.
• 6) Use "solve" to solve one dimensional problems like scattering off a well, a finite well (square or other interesting shapes), Can quickly do a finite square well in one class period. ( Pedagogical suggestion bring worksheet in and go through it during class). For the harmonic oscillator have Maple do the brute force and you do the elegant method with raising and lowering operators.
• 7) Hydrogen atom and other central potentials such as Yukawa, Lennard-Jones, Morse. Might want to compare the solutions for other central potentials with the hydrogen atom. Also other three-dimensional potentials such as the square well - it is actually r^n as n goes to infinity.
• 8) All the angular momentum "stuff". Use phi and theta equations already derived and then have them plot them and see what they look like.
• 9) Perturbation techniques: time independent, degenerate and non-degenerate. (Why do perturbation techniques when with Maple - do you really need it for one-dimensional or even three dimensional problems? Must understand the idea of perturbation theory - the concept of representing an arbitrary function in terms of a set of orthogonal functions. )
• 10) Matrix formulation of QM - Maple wonderful for manipulation of matrices. Even two-state problems can have quite tricky matrices.
• 11) Animation of the time-dependence of solutions; for example the solutions to the coupled square well, or make an arbitrary localized state and demonstrate what happens in time.
• 12) Classical probability density and quantum probability density approaching each other. Need to use coherent states - the Rydburg atom and the harmonic oscillator have potential.

Philosophy of Pedagogy:

• 1) GRAPH, GRAPH, GRAPH.
• 2) Model using Maple in the classroom as we use it as professionals. Set up the problem and describe the physical situation using pencil and paper turn to Maple to do the difficult and tedious computations.
• 3) Bring in overheads which show graphs (usually Maple) but then have the students go "home", bring down the appropriate Maple worksheet which show completely or incompletely how to do the problem. Their homework is an extension of the problem or a variation.
• 4) What are some real problems and sources for them that would require the use of Maple? There are some Russian problem books that might be good resources. Quark confinement/alpha decay are two specific suggestions.