Polar Wave Functions
The polar solutions graphed here are the unnormalized
associated Legendre polynomials, Plm(theta,phi). Refer to the convention accepted for spherical
coordinates. A positive angle theta is defined to
be the angle down from the z-axis toward the positive x-axis. The length
of a vector from the origin to the wave function is the magnitude of the wave
function at that angle.
Section 3 Exercises:
-
For any given values of l and ml,
observe that the plot does not change when ml is changed
to -ml. 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, zero, and a minimum. Explain
your results in terms of the formula for the wave function for this state. Also do
this for l = 2 and ml = 0 and l = 2 and ml
= 1.
Note:
Choosing the Show Multiple option and Resetting allows up to 4 plots to be
viewed simultaneously.
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Prentice-Hall, Inc. A Pearson Company