### Modern Physics Problem 10.2.1: Radial Wavefunctions

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#### Description

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.

#### Question

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.

#### Question

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.

#### Question

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*.

#### Credits

Physlet problems authored by Dan Boye. Script by Wolfgang Christian.