Note: Right click on either Physlet to make a copy. 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 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.
Make multiple plots of the wavefunctions. On which quantum numbers does the angular wavefunction depend? Be systematic. Change one number at a time.
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.
Notice the dependence of the number of lobes on l and ml. Obtain a general formula for this dependence.
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.
Physlet problems authored by Dan Boye. Script by Wolfgang Christian.