*Note: Right click on any applet to make a copy of the image. **The
mouse coordinates may be observed by left-clicking within the graph.*

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 a_{0} = 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 m? 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 your conclusion holds.

For a given principal quantum number, there is a maximum
value for *l*. The graph of the radial wave function in this
case should have only one maximum value. Obtain a general formula
relating the radius for this max value for all *n*.

Physlet problems authored by Dan Boye. Script by Wolfgang Christian. Modified locally by Scott Schneider.