Modern Physics Problem 10.2.1: Angular Wavefunctions

n =

 l =

m =

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Description

The two Physlets show a density  plot of the Hydrogenic wavefunction and the solution to the angular, that is, polar, 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 polar solutions used here are the unnormalized associated Legendre polynomials, Plm(q,f).  Note that the x and z coordinates range from -1 to +1.

Question

Make multiple plots of the wavefunctions.  On which quantum numbers does the angular wavefunction depend? Be systematic. Change one number at a time.

Question

For any given values of l and ml,  does the angular wavefunction change when ml is changed to -ml?  Does the total wavefunction change? Explain.

Question

Notice the dependence of the number of lobes on l and ml.  Obtain a general formula for this dependence.

Question

For l = 1 and ml = 0, determine the angles for which the wave function is a maximum and a minimum.  Explain your results in terms of the formula for the wave function for this state.

Credits

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