SCATTERING

Film Loop: Free Wave Packets

Length(min.):2:15, Color: No Sound: No

This computer-animated sequence shows a Gaussian wave packet in free space. The wave packet spreads out as time increases. The rate of spreading depends on the initial width of the packet. A packet initially very narrow spreads much more rapidly than one initially wide; both narrow and wide packets are shown simultaneously (see figure). Then, a stationary wave packet is compared to an identical but moving wave packet. The rate of spreading does not depend on the motion of the packets; both packets spread equally.

QUESTION: The figure shows the initial shape of two wave packets in X-space. What are the relative shapes of these same two packets in Phi-space? Reference might be made to 80-4039 which shows the time development of a wave packet scattering from a potential well in both X-space and Phi-space.

DISCUSSION: The horizontal coordinate in these displays is the X-axis, and the vertical coordinate is the position-probability density Phi(x,t)-squared. Detailed information concerning the formulation of the problem, integration techniques, initial conditions, and computer-input parameters has been published in American Journal of Physics35, 177 (March 1967); an alternative derivation has been published in the same journal, 36, 525 (June 1968).