Note: Right click on any applet to make a copy of the image. Choosing the Show Multiple option and Resetting allows up to 4 plots to be viewed simultaneously. The mouse coordinates may be observed by left-clicking within the graph.
The polar solutions graphed here are the unnormalized associated Legendre polynomials, P_{lm}(q,f). Refer to the convention accepted for spherical coordinates. A positive angle q 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.
For any given values of l and m_{l}, observe that the plot does not change when m_{l} is changed to -m_{l}. Explain.
Notice the dependence of the number of lobes on l and m_{l}. Obtain a general formula for this dependence.
For l = 1 and m_{l }= 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. Also do this for l = 2 and m_{l }= 0 and l = 2 and m_{l }= 1.