SCATTERING

Film Loop: Scattering in One Dimension - 2)Square Wells

Length(min.):2:40, Color: No, Sound: No

This computer-animated sequence shows the time development of a Gaussian wave packet as it moves into and out of the region of a finite square-potential well. The reflection from the well and the transmission through the well are shown for incident particle energies equal in magnitude to: (a) one-half the well depth (b) the well depth, and (c) twice the well depth.

DISCUSSION: The horizontal coordinate used in the display is the X-axis; the potential well is symmetrical about X = 0. For the well, the vertical coordinate is potential energy. For the wave packet the vertical coordinate is the position probability density Phi(x,t)-squared In each example the initial value of the probability density is the same even though the particle energy increases by a factor of two in each successive example. As the particle energy relative to the well potential increases, the reflected portion of the wave packet decreases and the rapid oscillations which appear when the packet is close to the potential (see figure) become less complex -- these are accurate solutions to the time-dependent Shrodinger equation and are not the result of computer error or programming approximations. Detailed information concerning the formulation of the problem, integration techniques, initial conditions, and computer input parameters has been published by American Journal of Physics, 35, 177 (March 1967).