This applet examines the properties of the wave functions for hydrogenic atoms. The top graphs are the wave functions generated by solutions of the polar and radial equations. Halliday and Resnick give only the radial (right hand plot) equations. They ignore the effect of angular momentum, which has separate solutions (left hand plot). The full solution is happily just the product of the radial and angular solutions. The polar solutions used here are the unnormalized associated Legendre polynomials, Plm(q,f). Note that the x and z coordinates range from -1 to +1. The radial solutions used here are the associated Laguerre polynomials scaled with a0 = 1. The graph in the lower left corner is a plot corresponding to the product of the upper two graphs.
The Physlets contained in this exercise package were written by Cabell Fisher, Jim Nolen, and Wolfgang Christian . This lab was prepared by Dan Boye.