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The two Physlets show a density plot of the Hydrogenic wavefunction and the solution to the radial equation. The word "density" refers to a method for plotting 3-D information on a two dimensional screen. Here it has nothing to do with the probability density in quantum mechanics. The radial solutions used here are the associated Laguerre polynomials scaled with the Bohr radius, a0 = 1.
Make multiple plots of the wavefunctions for n = 3. How is the behavior of the radial wavefunction for l = 0 different than for l = 1 or 2? Does the radial wavefunction depend on ml? Try this for a few other values for the principal quantum number and see if your conclusion holds.
For n = 3, how many times does the radial wave function cross zero (change signs) for each possible value of l? Try this for a few other values for the principal quantum number and see if you conclusion holds.
For a given principal quantum number n, there is a maximum value for l. The graph of the radial wave function in this case should have only one maximum value. Does this maximum value correspond to the value of the radius in the Bohr model? Check both small and very large values of n.
Physlet problems written by Dan Boye and modified by Paul Zitzewitz. Script by Wolfgang Christian.