Radial Wave Functions

The set of solutions to the radial equation can be found using standard methods of differential equations.  Notice that the radial solutions are determined by two quantum numbers n and l.  The solutions are the unnormalized associated Laguerre polynomials.  

Section 1 Exercises:

1. Make a multiple plot of the possible radial wave functions for n = 3.  How is the behavior for l = 0 different than for l = 1 or 2?  Try this for a few other values for the principal quantum number and see if your conclusion holds.
2. 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.
3. 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. 

Note: Choosing the Show Multiple option and Resetting allows up to 4 plots to be viewed simultaneously.

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