CONTINUUM COMPUTER SOLUTIONS OF THE SCHRODINGER-EQUATION

Computer integration of Schrodinger's time-independent wave equation with graphical display of solutions provides a valuable teaching aid, and is much used in the study of bound states. Much less attention has been paid to continuum solutions although these provide a richer set of phenomena. Programs are described that integrate the one-dimensional equation for potential steps and barriers, and model impedance matching, barrier penetration, and field emission. The radial equation for spherically symmetric potentials is also integrated and graphical demonstrations of scattering phase shifts, a simple model of the Ramsauer effect, and resonance scattering are provided. The programs have been used by undergraduates to investigate resonance scattering from spherical step and Woods-Saxon potentials, and a new power law relating resonance cross-section breadths and energies has been established.