and out in such a picture. What is the Schrdinger equation?Every quantum particle is characterized by a wave function. In 1925 Erwin Schrdinger developed the differential equation which describes the evolution of those wave functions. By using Schrdinger's equation scientists can find the wave function which solves a particular problem in quantum mechanics. Unfortunately, it is usually impossible to find an exact solution to the equation, so certain assumptions are used in order to obtain an approximate answer for the particular problem. What is a wave packet?As mentioned earlier, the Schrdinger equation for a particular problem cannot always be solved exactly. However, when there is no force acting upon a particle its potential energy is zero and the Schrdinger equation for the particle can be exactly solved. The solution to this 'free' particle is something known as a wave packet (which initially looks just like a Gaussian bell curve). Wave packets, therefore, can provide a useful way to find approximate solutions to problems which otherwise could not be easily solved.First, a wave packet is assumed to initially describe the particle under study. Then, when the particle encounters a force (so its potential energy is no longer zero), that force modifies the wave packet. The trick, of course, is to find accurate (and quick!) ways to 'propagate' the wave packet so that it still represents the particle at a later point in time. Finding such propagation techniques, and applying them to useful problems, is the topic of my current research. ReferencesClaude Cohen-Tannoudji, Bernard Diu, and Franck Lalo, Quantum Mechanics, Volumes 1 and 2, John Wiley & Sons, New York (1977). John J. Brehm and William J. Mullin, Introduction to the Structure of Matter: A Course in Modern Physics, John Wiley & Sons, New York (1989). Donald A. McQuarrie, Quantum Chemistry, University Science Books, Mill Valley, Calif. (1983). ------------------------------------...
