VISUALIZING THE SOLUTIONS FOR THE CIRCULAR INFINITE WELL IN QUANTUM AND CLASSICAL MECHANICS

The classical and quantum mechanical problem of a particle in the infi nite circular well has recently surfaced in two quite different manife stations: (i) the observation of ''electron standing waves'' in circul ar ''corrals'' of atoms adsorbed on surfaces and (ii) as a benchmark e xample of an integrable system for comparison to the classical and qua ntum chaotic behavior of the ''stadium billiards'' problem. Motivated by this, we review the quantum and classical probability distributions for both position and momentum for this familiar problem, focusing on ,the visualization of the quantum wave functions and classical traject ories as well as the semiclassical connections between the two. (C) 19 96 American Association of Physics Teachers.