Hydrogen Atom Wave Functions


This lab 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.  The polar solutions used here are the unnormalized associated Legendre polynomials, Plm(theta,phi).  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 two colors in the plots indicate the overall sign of the wave function: yellow (+) and blue(-).

The exercises are divided as follows: 

Section 1


Radial wave function

Section 2 Radial Integrals
Section 3 Angular wave function

Section 4

Density plots

Refer to Chapter 9 by Bernstein, Fishbane and Gasiorowicz  for a theoretical treatment of the hydrogen atom.

The Physlets contained in this exercise package were written by Cabell Fisher, Jim Nolen, and Wolfgang Christian .  This lab was prepared by Dan Boye.

2000 by Prentice-Hall, Inc. A Pearson Company